# Compositio Mathematica (COMPOS MATH )

Publisher: London Mathematical Society

## Description

The aim of Compositio Mathematica is to publish first class mathematical research papers. By tradition the journal focuses on papers in the main stream of pure mathematics. This includes the fields of algebra number theory topology algebraic and analytic geometry and (geometric) analysis. Papers on other topics are welcome if they are of interest to more than specialists alone. All contributions are required to meet high standards of quality and originality and are carefully screened by experts in the field.

• Impact factor
1.02
Show impact factor history

Impact factor
.
Year
• 5-year impact
1.24
• Cited half-life
0.00
• Immediacy index
0.09
• Eigenfactor
0.01
• Article influence
2.12
• Website
Compositio Mathematica website
• Other titles
Compositio mathematica
• ISSN
0010-437X
• OCLC
1564581
• Material type
Periodical, Internet resource
• Document type
Journal / Magazine / Newspaper, Internet Resource

## Publications in this journal

• ##### Article: The $cd$-index of fans and posets
Compositio Mathematica 01/2006; 142(3):701-718.
• Source
##### Article: Weighted Completion of Galois Groups and Galois Actions on the Fundamental Group of P1 - {0,1, ∞}
[hide abstract]
ABSTRACT: Fix a prime number . We prove a conjecture stated by Ihara, which he attributes to Deligne, about the action of the absolute Galois group on the pro- completion of the fundamental group of the thrice punctured projective line. Similar techniques are also used to prove part of a conjecture of Goncharov, also about the action of the absolute Galois group on the fundamental group of the thrice punctured projective line. The main technical tool is the weighted completion of a profinite group with respect to a reductive representation (and other appropriate data).
Compositio Mathematica 10/2003; 139(2):119-167.
• Source
##### Article: Differential Modular Forms on Shimura Curves, I
[hide abstract]
ABSTRACT: The quotient of a Shimura curve by the isogeny equivalence relation is not an object of algebraic geometry. The paper shows how this quotient space becomes a geometric object in a more general geometry obtained from 'usual algebraic geometry', by adjoining a new operation; this operation looks like a 'Fermat quotient' and should be viewed as an arithmetic analogue of usual derivations.
Compositio Mathematica 10/2003; 139(2):197-237.
• Source
##### Article: The Speciality Lemma, Rank 2 Bundles and Gherardelli-type Theorems for Surfaces in P4
[hide abstract]
ABSTRACT: In the present paper we give a very short and easy proof of the speciality lemma for codimension 2 subvarieties, even those that are reducible or non-reduced, in P n . Furthermore we give cohomological conditions that force a subcanonical surface in P 4 to be a complete intersection and a rank 2 bundle to split, which generalize the classical First Theorem of Gherardelli.
Compositio Mathematica 09/2003; 139(1):101-111.
• Source
##### Article: Stickelberger elements for cyclic extensions and the order of vanishing of Abelian L-functions at s=O
[hide abstract]
ABSTRACT: We study the Stickelberger element of a cyclic extension of global fields of prime power degree. Assuming that S contains an almost splitting place, we show that the Stickelberger element is contained in a power of the relative augmentation ideal whose exponent is at least as large as Gross's prediction. This generalizes the work of Tate (see Section 4) on a refinement of Gross's conjecture in the cyclic case. We also present an example for which Tate's prediction does not hold.
Compositio Mathematica 09/2003;
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##### Article: A Sato–Tate Law for Drinfeld Modules
[hide abstract]
ABSTRACT: We formulate and prove a Sato–Tate equidistribution law for Drinfeld modules.
Compositio Mathematica 08/2003; 138(2):189-197.
• Source
##### Article: Towards Bounding Complexity of a Minimal Model
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ABSTRACT: We give some effectivity results in birational geometry. We provide an upper bound on the rational constant in Rationality Theorem in terms of certain intersection numbers, under an additional condition on the variety that it admits a divisorial contraction. One consequence is an explicit bound on the number of certain extremal rays. Our main result tries to construct from a given set of ample divisors H j on X with their intersection numbers b i , a certain set of ample divisors L j on X'' or X + where X'' or X + arises from a contraction or a flip,such that the corresponding intersection numbers of L j are uniformly bounded in terms of b i and the index of X. This gives a bound on the projective degree of a minimal model in special case.
Compositio Mathematica 08/2003; 138(3):245-260.
• Source
##### Article: Equisingular Deformations of Sandwiched Singularities
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ABSTRACT: We relate the equisingular deformation theory of plane curve singularities and sandwiched surface singularities. We show the existence of a smooth map between the two corresponding deformation functors and study the kernel of this map. In particular we show that the map is an isomorphism when a certain invariant is large enough.
Compositio Mathematica 08/2003; 138(2):199-231.
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##### Article: Sur quelques représentations modulaires et p-adiques de GL2(Qp): I
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ABSTRACT: Let p be a prime number and F a complete local field with residue field of characteristic p. In 1993, Barthel and Livn proved the existence of a new kind of [(F)]p{\bar F_p } -representations of GL2(F) that they called 'supersingular' and on which one knows almost nothing. In this article, we determine all the supersingular representations of GL2(Q p ) with their intertwinings. This classification shows a natural bijection between the set of isomorphism classes of supersingular representations of GL2(Q p ) and the set of isomorphism classes of two-dimensional irreducible [(F)]p{\bar F_p } -representations of Gal( [`(Q)]p /Qp ){Gal}\left( {{\bar Q}_p /{Q}_p } \right) .
Compositio Mathematica 08/2003; 138(2):165-188.
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##### Article: On the Iwasawa Theory of p-Adic Lie Extensions
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ABSTRACT: In this paper, the new techniques and results concerning the structure theory of modules over noncommutative Iwasawa algebras are applied to arithmetic: we study Iwasawa modules over p-adic Lie extensions k of number fields k 'up to pseudo-isomorphism'. In particular, a close relationship is revealed between the Selmer group of Abelian varieties, the Galois group of the maximal Abelian unramified p-extension of k as well as the Galois group of the maximal Abelian p-extension unramified outside S where S is a certain finite setof places of k. Moreover, we determine the Galois module structure of local units and other modules arising from Galois cohomology.
Compositio Mathematica 07/2003; 138(1):1-54.
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##### Article: Almost Squares and Factorisations in Consecutive Integers
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ABSTRACT: We show that there is no square other than 122 and 7202 such that it can be written as a product of k–1 integers out of k(3) consecutive positive integers. We give an extension of a theorem of Sylvester that a product of k consecutive integers each greater than k is divisible by a prime exceeding k.
Compositio Mathematica 07/2003; 138(1):113-124.
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##### Article: Almost Squares in Arithmetic Progression
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ABSTRACT: It is proved that a product of four or more terms of positive integers in arithmetic progression with common difference a prime power is never a square. More general results are given which completely solve (1.1) with gcd(n, d)=1, k3 and 1d104.
Compositio Mathematica 07/2003; 138(1):73-111.
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##### Article: Equidistribution of Integer Points on a Family of Homogeneous Varieties: A Problem of Linnik
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ABSTRACT: We study an equidistribution problem of Linnik using Hecke operators.
Compositio Mathematica 04/2003; 136(3):323-352.
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##### Article: The Local Stark Conjecture at a Real Place
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ABSTRACT: A refinement of the rank 1 Abelian Stark conjecture has been formulated by B.Gross. This conjecture predicts some \mathfrakp\mathfrak{p} -adic analytic nature of a modification of the Stark unit. The conjecture makes perfect sense even when \mathfrakp\mathfrak{p} is an Archimedean place. Here we consider the conjecture when \mathfrakp\mathfrak{p} is a real place, and interpret it in terms of 2-adic properties of special values of L-functions. We prove the conjecture for CM extensions; here the original Stark conjecture is uninteresting, but the refined conjecture is nontrivial. In more generality, we show that, under mild hypotheses, if the subgroup of the Galois group generated by complex conjugations has less than full rank, then the refined conjecture implies that the Stark unit should be a square. This phenomenon has been discovered by Dummit and Hayes in a particular type of situation. We show that it should hold in much greater generality.
Compositio Mathematica 04/2003; 137(1):75-90.
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##### Article: A Taylor–Wiles System for Quaternionic Hecke Algebras
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ABSTRACT: Let &ell >3 be a prime. Fix a regular character of F&2 of order &–1, and an integer M prime to &. Let fS 2(0(M&2)) be a newform which is supercuspidal of type at &. For an indefinite quaternion algebra over Q of discriminant dividing the level of f, there is a local quaternionic Hecke algebra T of type associated to f. The algebra T acts on a quaternionic cohomological module M. We construct a Taylor–Wiles system for M, and prove that T is the universal object for a deformation problem (of type at & and semi-stable outside) of the Galois representation f over F& associated to f; that T is complete intersection and that the module M is free of rank 2 over T. We deduce a relation between the quaternionic congruence ideal of type for f and the classical one.
Compositio Mathematica 04/2003; 137(1):23-47.
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##### Article: Index Formulas for Ramified Elliptic Units
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ABSTRACT: We compute the index of certains groups of elliptic units. These groups are the analoguousof Sinnott's groups of circular units.
Compositio Mathematica 04/2003; 137(1):1-22.
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##### Article: Riemann–Roch for Algebraic Stacks: I
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ABSTRACT: In this paper we establish Riemann–Roch and Lefschtez–Riemann–Roch theorems for arbitrary proper maps of finite cohomological dimension between algebraic stacks in the sense of Artin. The Riemann–Roch theorem is established as a natural transformation between the G-theory of algebraic stacks and topological G-theory for stacks: we define the latter as the localization of G-theory by topological K-homology. The Lefschtez–Riemann–Roch is an extension of this including the action of a torus for Deligne–Mumford stacks. This generalizes the corresponding Riemann–Roch theorem (Lefschetz–Riemann–Roch theorem) for proper maps between schemes (that are also equivariant for the action of a torus, respectively) making use of some fundamental results due to Vistoli and Toen. A key result established here is that topological G-theory (as well as rational G-theory) has cohomological descent on the isovariant tale site of an algebraic stack. This extends cohomological descent for topological G-theory on schemes as proved by Thomason.
Compositio Mathematica 03/2003; 136(2):117-169.

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