# Journal of Pure and Applied Algebra

Published by Elsevier

Print ISSN: 0022-4049

Published by Elsevier

Print ISSN: 0022-4049

Publications

Almost all of the categories normally used as a mathematical foundation for denotational semantics satisfy a condition known as consistent completeness. The authors explore the possibility of using different condition coherence, which has its origin in topology and logic. In particular, they concentrate on posets with principal ideas that are algebraic lattices and with coherent topologies. These form a Cartesian closed category which has fixed points for domain equations. It is shown that a universal domain exists. A categorical treatment of the construction of this domain is provided, and its relationship to other applications discussed.< >

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- 19 Reads
- 25 Citations

We establish model category structures on algebras and modules over operads and non-Σ operads in monoidal model categories. The results have applications in algebraic topology, stable homotopy theory, and homological algebra.

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- 31 Reads
- 27 Citations

We classify rank two Fano bundles over the Grassmannian of lines $\G(1,4)$.
In particular we show that the only non-split rank two Fano bundle over
$\G(1,4)$ is, up to a twist, the universal quotient bundle $\cQ$. This
completes the classification of rank two Fano bundles over Grassmannians of
lines.

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- 32 Reads
- 4 Citations

A Gorenstein sequence H is a sequence of nonnegative integers H=(1,h1,…,hj=1) symmetric about j/2 that occurs as the Hilbert function in degrees less or equal j of a standard graded Artinian Gorenstein algebra A=R/I, where R is a polynomial ring in r variables and I is a graded ideal. The scheme PGor(H) parametrizes all such Gorenstein algebra quotients of R having Hilbert function H and it is known to be smooth when the embedding dimension satisfies h1⩽3. The authors give a structure theorem for such Gorenstein algebras of Hilbert function H=(1,4,7,…) when R=K[w,x,y,z] and I2≅〈wx,wy,wz〉 (Theorems 3.7 and 3.9). They also show that any Gorenstein sequence H=(1,4,a,…),a⩽7 satisfies the condition ΔH⩽j/2 is an O-sequence (Theorems 4.2 and 4.4). Using these results, they show that if H=(1,4,7,h,b,…,1) is a Gorenstein sequence satisfying 3h-b-17⩾0, then the Zariski closure of the subscheme C(H)⊂PGor(H) parametrizing Artinian Gorenstein quotients A=R/I with I2≅〈wx,wy,wz〉 is a generically smooth component of PGor(H) (Theorem 4.6).They show that if in addition 8⩽h⩽10, then such PGor(H) have several irreducible components (Theorem 4.9). M. Boij and others had given previous examples of certain PGor(H) having several components in embedding dimension four or more (Pacific J. Math. 187(1) (1999) 1–11).The proofs use properties of minimal resolutions, the smoothness of PGor(H′) for embedding dimension three (J.O. Kleppe, J. Algebra 200 (1998) 606–628), and the Gotzmann Hilbert scheme theorems (Math. Z. 158(1) (1978) 61–70).

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- 50 Reads
- 34 Citations

According to a conjecture of H. Clemens, the dimension of the space of
rational curves on a general projective hypersurface should equal the number
predicted by a na\"ive dimension count. In the case of a general hypersurface
of degree 7 in $\mathbb{P}^5$, the conjecture predicts that the only rational
curves should be lines. This has been verified by Hana and Johnsen for rational
curves of degree at most 15. Here we extend their results to show that no
rational curves of degree 16 lie on a general heptic fourfold.

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- 31 Reads
- 1 Citation

Sufficient conditions for an ideal $\mathcal I$ in $R\Mod$ to be covering are
proved. This allows to obtain an alternative proof of the existence of phantom
covers of modules. Our approach is inspired by an extension of the standard
deconstructibility techniques used in Approximation Theory.

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- 49 Reads
- 18 Citations

Up until now, it was recognized that a large number of 2-torsion points was a
technical barrier to improve the bounds for the symmetric tensor rank of
multiplication in every extension of any finite field. In this paper, we show
that there are two exceptional cases, namely the extensions of $\mathbb{F}_2$
and $\mathbb{F}_3$. In particular, using the definition field descent on the
field with 2 or 3 elements of a Garcia-Stichtenoth tower of algebraic function
fields which is asymptotically optimal in the sense of Drinfel'd-Vladut and has
maximal Hasse-Witt invariant, we obtain a significant improvement of the
uniform bounds for the symmetric tensor rank of multiplication in any extension
of $\mathbb{F}_2$ and $\mathbb{F}_3$.

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- 32 Reads
- 5 Citations

Let R be a one-dimensional noetherian domain containing the field Q of rational numbers. Let A be an A2-fibration over R. Then there exists HϵA such that A is an A1-fibration over R[H]. As a consequence, if is free then A = R[2].

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- 14 Reads
- 19 Citations

We use the Z-algebra theory developed by J. Lepowsky and R. Wilson to study the structure of level three standard modules for the affine Lie algebra A2(2) in the principal picture. We get their linear bases in terms of Z-operators. As a consequence we give Z-algebra proofs of the conjectures of Capparelli (1993) on two combinatorial identities.

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- 18 Reads
- 31 Citations

We define the tensor product of filtered $A_\infty$-algebras. establish some
of its properties and give a partial description of the space of bounding
cochains in the tensor product. Furthermore we show that in the case of
classical $A_\infty$-algebras our definition recovers the one given by Markl
and Shnider. We also give a criterion that implies that a given
$A_\infty$-algebra is quasi-isomorphic to the tensor product of two
subalgebras. This will be used in a sequel to prove a K\"unneth Theorem for the
Fukaya algebra of a product of Lagrangian submanifolds.

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- 73 Reads
- 17 Citations

Recently, the first Abel map for a stable curve of genus g≥2 has been constructed. Fix an integer d≥1 and let C be a stable curve of compact type of genus g≥2. We construct two d-th Abel maps for C, having different targets, and we compare the fibers of the two maps. As an application, we get a characterization of hyperelliptic stable curves of compact type with two components via the second Abel map.

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- 42 Reads
- 26 Citations

We study the relation between Bourn's notion of peri-abelian category and
conditions involving the coincidence of the Smith, Huq and Higgins commutators.
In particular we show that a semi-abelian category is peri-abelian if and only
if for each normal subobject $K\leq X$, the Higgins commutator of $K$ with
itself coincides with the normalisation of the Smith commutator of the
denormalisation of $K$ with itself. We show that if a category is peri-abelian,
then the condition (UCE), which was introduced and studied by Casas and the
second author, holds for that category. In addition we show, using amongst
other things a result by Cigoli, that all categories of interest in the sense
of Orzech are peri-abelian and therefore satisfy the condition (UCE).

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- 52 Reads
- 7 Citations

In this paper, we study precompact abelian groups G that contain no sequence
{x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G,
and x_n --> 0. We characterize groups with this property in the following
classes of groups:
(a) bounded precompact abelian groups;
(b) minimal abelian groups;
(c) totally minimal abelian groups;
(d) \omega-bounded abelian groups.
We also provide examples of minimal abelian groups with this property, and
show that there exists a minimal pseudocompact abelian group with the same
property; furthermore, under Martin's Axiom, the group may be chosen to be
countably compact minimal abelian.

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- 33 Reads
- 8 Citations

Basing ourselves on the concept of double central extension from categorical
Galois theory, we study a notion of commutator which is defined relative to a
Birkhoff subcategory B of a semi-abelian category A. This commutator
characterises Janelidze and Kelly's B-central extensions; when the subcategory
B is determined by the abelian objects in A, it coincides with Huq's
commutator; and when the category A is a variety of omega-groups, it coincides
with the relative commutator introduced by the first author.

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- 83 Reads
- 26 Citations

Let $A$ be a unital associative algebra over a field $k$, $E$ a vector space
and $\pi : E \to A$ a surjective linear map with $V = {\rm Ker} (\pi)$. All
algebra structures on $E$ such that $\pi : E \to A$ becomes an algebra map are
described and classified by an explicitly constructed global cohomological type
object ${\mathbb G} {\mathbb H}^{2} \, (A, \, V)$. Any such algebra is
isomorphic to a Hochschild product $A \star V$, an algebra introduced as a
generalization of a classical construction. We prove that ${\mathbb G} {\mathbb
H}^{2} \, (A, \, V)$ is the coproduct of all non-abelian cohomologies ${\mathbb
H}^{2} \, \, (A, \, (V, \cdot))$. The key object ${\mathbb G} {\mathbb H}^{2}
\, (A, \, k)$ responsible for the classification of all co-flag algebras is
computed. All Hochschild products $A \star k$ are also classified and the
automorphism groups ${\rm Aut}_{\rm Alg} (A \star k)$ are fully determined as
subgroups of a semidirect product $A^* \, \ltimes \bigl(k^* \times {\rm
Aut}_{\rm Alg} (A) \bigl)$ of groups. Several examples are given as well as
applications to the theory of supersolvable coalgebras or Poisson algebras. In
particular, for a given Poisson algebra $P$, all Poisson algebras having a
Poisson algebra surjection on $P$ with a $1$-dimensional kernel are described
and classified.

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- 22 Reads
- 5 Citations

For any finite abelian group G, we study the moduli space of abelian
$G$-covers of elliptic curves, in particular identifying the irreducible
components of the moduli space. We prove that, in the totally ramified case,
the moduli space has trivial rational Picard group, and it is birational to the
moduli space M_{1,n}, where n is the number of branch points. In the particular
case of moduli of bielliptic curves, we also prove that the boundary divisors
are a basis of the rational Picard group of the admissible covers
compactification of the moduli space. Our methods are entirely
algebro-geometric.

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- 25 Reads
- 5 Citations

We study the geometry of abelian subgroups relative to combings (normal forms) of automatic groups and groups which act properly and cocompactly on spaces of nonpositive curvature. We prove that in general combings which arise in the latter context are incompatible (in a sense which we make precise) with regular combings, the fundamental objects of automatic group theory.

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- 22 Reads
- 11 Citations

We prove that for each ℓ-group G, the topological space Spec(G) satisfies a condition Idω. Generalising a previous construction of Delzell and Madden we show that for each nondenumer-able cardinal there is a completely normal spectral space that is not homeomorphic to Spec(G) for any ℓ-group G. We show also that a stronger form of property Idω, called Id, suffices to ensure that a completely normal spectral space is homeomorphic to Spec(G) for some ℓ-group G.

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- 9 Reads
- 19 Citations

We show that every Abelian group G with r0(G)=|G|=|G|ω admits a pseudocompact Hausdorff topological group topology T such that the space (G,T) is Fréchet–Urysohn. We also show that a bounded torsion Abelian group G of exponent n admits a pseudocompact Hausdorff topological group topology making G a Fréchet–Urysohn space if for every prime divisor p of n and every integer k≥0, the Ulm–Kaplansky invariant fp,k of G satisfies (fp,k)ω=fp,k provided that fp,k is infinite and fp,k>fp,i for each i>k.Our approach is based on an appropriate dense embedding of a group G into a Σ-product of circle groups or finite cyclic groups.

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- 44 Reads
- 7 Citations

For a fixed proper subgroup R (of type t) of the group of rational numbers, a torsion-free group A is called an R-group if it satisfies Bext1(A, R) = 0, where Bext stands for the set of balanced extensions. Those R-groups whose nonzero elements are of types ≤t are investigated. In the constructible universe L, these R-groups (up to cardinality ℵω) turn out to coincide with those A for which the group is a Butler group; here R0 denotes the largest subgroup of R of idempotent type . This claim is false in models of set theory in which Shelah's Proper Forcing Axiom holds.

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- 8 Reads
- 5 Citations

In this paper we show that a direct summand of a simply presented mixed abelain group is an almost affable group. As a consequence, the classification theorem due to the author is extended to the largest possible class.

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- 11 Reads
- 10 Citations

In the context of semi-abelian categories, we develop some new xaspects of the categorical theory of central extensions by Janelidze and Kelly. If is a semi-abelian category and is any admissible subcategory we give several characterizations of trivial and central extensions. The notion of central extension becomes intrinsic when is the subcategory of the abelian objects in . We apply these results to the category of internal groupoids in a semi-abelian category. As a very special case, we get the known description of central extensions for crossed modules.

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- 62 Reads
- 49 Citations

We study the locus of abelian Galois covers of $\mathbb{P}^{1}$ in $A_{g}$
and the problem of occurrence of Shimura (special) subvarieties generated by
these covers in the Torelli locus $T_{g}$ inside $A_{g}$. We first investigate
the existence of Shimura subvarieties in the mentioned locus by some
computational methods based on Moonen-Oort works and then exclude many cases
using both characteristic $p$ methods and monodromy computations.

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- 29 Reads
- 27 Citations

We prove that every countable subgroup of a compact metrizable abelian group has a characterizing set. As an application, we answer several questions on maximally almost periodic (MAP) groups and give a characterization of the class of (necessarily MAP) abelian topological groups whose Bohr topology has countable pseudocharacter.

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- 32 Reads
- 35 Citations

A ring R is said to be a unique addition ring (UA-ring) if any semigroup isomorphism R∗ = (R, ∗) ∼- (S, ∗) = S∗ of multiplicative semigroups with another ring S is always a ring isomorphism. See [5, 7–9] for earlier work on UA-rings. Depending on the context, we may or may not regard 0 as an element of R∗. An abelian group G is called a UA-group if its endomorphism ring E(G) is a UA-ring. Given an abelian group G, denote by E∗(G) the semigroup of all endomorphisms of G and let RG be the collection of all rings R such that R∗ ∼- E∗(G). The group G is said to be an if for every ring (E∗(G), ⊕), where ⊕ is an addition on the semigroup E∗(G), there is an abelian group H such that (E∗(G), ⊕) is (isomorphic to) the endomorphism ring of H. Equivalently, G is an if for every ring R in RG there is an abelian group H such that R is (isomorphic to) the endomorphism ring of H.Section 1 is a study of separable torsion-free abelian UA-groups. In Section 2 we develop necessary and sufficient conditions for a torsion-free separable group to be an . All groups are abelian.

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- 17 Reads
- 6 Citations

The class of finitely presented algebras over a field K with a set of generators a_1,...,a_n and defined by homogeneous relations of the form a_1a_2...a_n = a_{sigma(1)}a_{sigma(2)}...a_{sigma(n)}, where sigma runs through an abelian subgroup H of Sym_{n}, the symmetric group, is considered. It is proved that the Jacobson radical of such algebras is zero. Also, it is characterized when the monoid S_n(H), with the "same" presentation as the algebra, is cancellative in terms of the stabilizer of 1 and the stabilizer of n in H. This work is a continuation of earlier work of Cedo, Jespers and Okninski. Comment: 15 pages

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- 42 Reads
- 5 Citations

In this paper we determine the number of isomorphism classes of superspecial abelian varieties $A$ over the prime field $\Fp$ such that the relative Frobenius morphism $\pi_A$ satisfying $\pi_A^2=-p$. Comment: 12 pages, revised version

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- 23 Reads
- 9 Citations

We introduce a categorical closure operator g in the category of topological abelian groups (and continuous homomorphisms) as a Galois closure with respect to an appropriate Galois correspondence defined by means of the Pontryagin dual of the underlying group. We prove that a topological abelian group G is maximally almost periodic if and only if every cyclic subgroup of G is g-closed. This generalizes a property characterizing the circle group from (Studia Sci. Math. Hungar. 38 (2001) 97–113, A characterization of the circle group and the p-adic integers via sequential limit laws, preprint), and answers an appropriate version of a question posed in (A characterization of the circle group and the p-adic integers via sequential limit laws, preprint).

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- 43 Reads
- 48 Citations

We obtain necessary and sufficient conditions for abelian varieties to acquire semistable reduction over fields of low degree. Our criteria are expressed in terms of torsion points of small order defined over unramified extensions.

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- 11 Reads
- 5 Citations

We characterize the maximum r-local index of a Schur algebra over an abelian number field K in terms of global information determined by the field K for an arbitrary rational prime, r. This completes and unifies previous results of Janusz in [G.J. Janusz, The Schur group of an algebraic number field, Ann. of Math. (2) 103 (1976) 253–281] and Pendergrass in [J.W. Pendergrass, The 2-part of the Schur group, J. Algebra 41 (1976) 422–438].

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- 38 Reads
- 1 Citation

In this paper we discuss multiplicative relations between eigenvalues of
Frobenius endomorphism of abelian varieties of small dimension over finite
fields.

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- 72 Reads
- 11 Citations

We define admissible abelian categories and compute the K-theory of such categories, with the aim to study and compute the K-groups of noncommutative rings and other noncommutative situations. One of the main results of this dissertation is the localization theorem.

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- 11 Reads
- 19 Citations

We prove a Dold–Kan type correspondence between the category of planar dendroidal abelian groups and a suitably constructed category of planar dendroidal chain complexes. Our result naturally extends the classical Dold–Kan correspondence between the category of simplicial abelian groups and the category of non-negatively graded chain complexes.

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- 60 Reads
- 17 Citations

Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective lines; this is illustrated by various applications. Comment: 14 pages

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- 20 Reads
- 19 Citations

The quasi-Baer-splitting property is extended from self-small torsion free groups to arbitrary self-small abelian groups. The self-small group A has this property iff it is almost-faithful as an E-module. This fact is reflected in the structure of A/t(A) as a module over the Walk-endomorphism ring of A. A self-small group A is almost E-flat and has the quasi-Baer-splitting property iff the class of almost A-adstatic modules is closed with respect to submodules and iff A is “almost-projective” with respect to the class of almost A-static groups.

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- 11 Reads
- 3 Citations

We examine the homotopy theory of simplicial graded abelian Hopf algebras over a prime field Fp, p > 0, proving that two very different notions of weak equivalence yield the same homotopy category. We then prove a splitting result for the Postnikov tower of such simplicial Hopf algebras. As an application, we show how to recover the homotopy groups of a simplicial Hopf algebra from its André-Quillen homology, which, in turn, can be easily computed from the homotopy groups of the associated simplicial Dieudonné module.

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- 21 Reads
- 4 Citations

We show that if A1, A2,..., An, B1, B2,...,Bt are uniform objects of an abelian category C, then A1 ⊕ A2 ⊕⋯⊕ An and B1 ⊕ B2 ⊕⋯⊕ Bt are in the same monogeny class if and only if n = t and there is a permutation σ of 1, 2,...,n} such that Ai and Bσ(i) are in the same monogeny class for every i = 1, 2,..., n. This is proved by showing that strong components of bipartite digraphs with enough edges intersect the two independent sets of vertices of a bipartition of the digraph in sets of the same cardinality.

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- 18 Reads
- 16 Citations

We prove that direct and inverse limits of sequences of reflexive Abelian groups that are metrizable or kω-spaces, but not necessarily locally compact, are reflexive and dual of each other provided some extra conditions are satisfied by the sequences.

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- 37 Reads
- 12 Citations

Some categories of groups (typically involving groups, possibly infinite, with abelian Frobenius kernels) are shown to be equivalent to categories whose objects are modules over groups and rings. The rings in question are associated with algebraic number fields, and the category equivalences allow some applications of number theory to group theory. In particular the number of isomorphism classes of metabelian Frobenius groups with kernel of order n and complement of order m is calculated in terms of the prime factorization of n and the structure of the Euler group .

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- 16 Reads
- 4 Citations

Let G be a connected reductive group defined over an algebraically closed field k of characteristic p>0. The purpose of this paper is two-fold. First, when p is a good prime, we give a new proof of the “order formula” of Testerman for unipotent elements in G; moreover, we show that the same formula determines the p-nilpotence degree of the corresponding nilpotent elements in the Lie algebra of G. Second, if G is semisimple and p is sufficiently large, we show that G always has a faithful representation (ρ,V) with the property that the exponential of dρ(X) lies in ρ(G) for each p-nilpotent . This property permits a simplification of the description given by Suslin et al. of the (even) cohomology ring for the Frobenius kernels . The previous authors already observed that the natural representation of a classical group has the above property (with no restriction on p). Our methods apply to any Chevalley group and hence give the result also for quasisimple groups with “exceptional type” root systems. The methods give explicit sufficient conditions on p; for an adjoint semisimple G with Coxeter number h, the condition p>2h−2 is always good enough.

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- 22 Reads
- 33 Citations

An abelian group G is almost A-solvable if the natural map θG:Hom(A,G)⊗E(A)A→G is a quasi-isomorphism. Two strongly indecomposable torsion-free abelian groups A and B of finite rank are quasi-isomorphic if and only if the classes of almost A-solvable and almost B-solvable groups coincide. Homological properties of almost A-solvable groups are described, and several examples are given. In particular, there exists a torsion-free almost A-solvable group which is not quasi-isomorphic to an A-solvable group.

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- 15 Reads
- 3 Citations

Let $\mathfrak{Var}_k^G$ denote the category of pairs $(X,\sigma)$, where $X$
is a variety over $k$ and $\sigma$ is a group action on $X$. We define the
Grothendieck ring for varieties with group actions as the free abelian group of
isomorphism classes in the category $\mathfrak{Var}_k^G$ modulo a cutting and
pasting relation. The multiplication in this ring is defined by the fiber
product of varieties. This allows for motivic zeta-functions for varieties with
group actions to be defined. This is a formal power series
$\sum_{n=0}^{\infty}[\text{Sym}^n (X,\sigma)]t^n$ with coefficients in the
Grothendieck ring. The main result of this paper asserts that the motivic
zeta-function for an algebraic curve with a finite abelian group action is
rational. This is a partial generalization of Weil's First Conjecture.

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- 31 Reads
- 4 Citations

We show that certain abelian varieties A have the property that for every
Hodge structure V in the cohomology of A, every effective Tate twist of V
occurs in the cohomology of some abelian variety. We deduce the general Hodge
conjecture for certain non-simple abelian varieties of type IV.

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- 21 Reads
- 3 Citations

In this paper, the main objective is to compare the abelian subalgebras and
ideals of maximal dimension for finite-dimensional supersolvable Lie algebras.
We characterise the maximal abelian subalgebras of solvable Lie algebras and
study solvable Lie algebras containing an abelian subalgebra of codimension 2.
Finally, we prove that nilpotent Lie algebras with an abelian subalgebra of
codimension 3 contain an abelian ideal with the same dimension, provided that
the characteristic of the underlying field is not two. Throughout the paper, we
also give several examples to clarify some results.

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- 158 Reads
- 13 Citations

We prove that any abelian variety with CM by OL of characteristic p is defined over a finite field, where OL is the ring of integers of the CM field L. This generalizes a theorem of Grothendieck on isogeny classes of CM abelian varieties. We also provide a direct proof of the Grothendieck theorem, which does not require several ingredients based on Weil's foundation as the original proof does. A description of the isomorphism classes is given. We analyze the reduction map modulo p for the abelian varieties concerned and solve the lifting and algebraization problem.

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- 49 Reads
- 20 Citations

We develop some new aspects of cohomology in the context of semi-abelian categories: we establish a Hochschild-Serre 5-term exact sequence extending the classical one for groups and Lie algebras; we prove that an object is perfect if and only if it admits a universal central extension; we show how the second Barr-Beck cohomology group classifies isomorphism classes of central extensions; we prove a universal coefficient theorem to explain the relationship with homology. (c) 2007 Elsevier B.V. All rights reserved.

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- 39 Reads
- 34 Citations

We give results on when homomorphisms between abelian varieties are or are not defined over fields obtained from division points on the varieties. For example, if A and B are abelian varieties defined over a field F, of dimensions d and e, respectively, and L is the intersection of the fields F(AN, BN) for all integers N prime to the characteristic of F and greater than 2, then every element of Hom(A, B) is defined over L, is unramified at the discrete places of good reduction for A × B, and [L : F] divides H(d,e), where H(d,e) is a number given by an explicit formula and is less than 4(9d)2d(9e)2e.

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- 21 Reads
- 81 Citations

Let φ be a Drinfeld module defined over a finite extension K of the rational function field , we show that the submodule φ(Kab)tors of all torsion points in the maximal abelian extension Kab is infinite if and only if φ is of complex multiplication type over K.

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- 22 Reads
- 9 Citations

We study the moduli space Sg(a) of principally polarized supersingular abelian varieties of dimension g with a-number a. We determine the dimension of each irreducible component of Sg(a) and the number of irreducible components.

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- 7 Reads
- 4 Citations

For a compact Hausdorff abelian group K and its subgroup H≤K, one defines the g-closuregK(H) of H in K as the subgroup consisting of χ∈K such that χ(an)⟶0 in T=R/Z for every sequence {an} in (the Pontryagin dual of K) that converges to 0 in the topology that H induces on . We prove that every countable subgroup of a compact Hausdorff group is g-closed, and thus give a positive answer to two problems of Dikranjan, Milan and Tonolo. We also show that every g-closed subgroup of a compact Hausdorff group is realcompact. The techniques developed in the paper are used to construct a close relative of the closure operator g that coincides with the Gδ-closure on compact Hausdorff abelian groups, and thus captures realcompactness and pseudocompactness of subgroups.

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- 21 Reads
- 3 Citations

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