Compositio Mathematica (COMPOS MATH )
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 factor1.02Show impact factor historyImpact factorYear
 5year impact1.24
 Cited halflife0.00
 Immediacy index0.09
 Eigenfactor0.01
 Article influence2.12
 WebsiteCompositio Mathematica website
 Other titlesCompositio mathematica
 ISSN0010437X
 OCLC1564581
 Material typePeriodical, Internet resource
 Document typeJournal / Magazine / Newspaper, Internet Resource
Publications in this journal
 Compositio Mathematica 07/2014; 150(7).
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ABSTRACT: We formulate a conjecture which generalizes Darmon's "refined class number formula". We discuss relations between our conjecture and the equivariant leading term conjecture of Burns. As an application, we give another proof of the "except 2part" of Darmon's conjecture, which was first proved by Mazur and Rubin.Compositio Mathematica 06/2014; 
Article: Dmodules on spaces of rational maps
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ABSTRACT: Let X be an algebraic curve. We study the problem of parametrizing geometric structures over X which are only generically defined. For example, parametrizing generically defined maps (rational maps) from X to a fixed target scheme Y. There are three methods for constructing functors of points for such moduli problems (all originally due to Drinfeld), and we show that the resulting functors are equivalent in the fppf Grothendieck topology. As an application, we obtain three presentations for the category of Dmodules ‘on’ B(K)∖G(𝔸)/G(𝕆), and we combine results about this category coming from the different presentations.Compositio Mathematica 05/2014; 150(5).  Compositio Mathematica 04/2014; 150(4).

Article: Higher Chow cycles on abelian surfaces and a nonArchimedean analogue of the HodgeDconjecture
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ABSTRACT: We construct new indecomposable elements in the higher Chow group CH 2 (A,1) of a principally polarized Abelian surface over a padic local field, which generalize an element constructed by Collino [Griffiths’ infinitesimal invariant and higher Ktheory on hyperelliptic Jacobians, J. Algebraic Geom. 6 (1997), 393415]. These elements are constructed using a generalization, due to Birkenhake and Wilhelm [HumbertsurfacesandtheKummerplane, Trans. Amer. Math. Soc. 355 (2003), 18191841 (electronic)], of a classical construction of Humbert. They can be used to prove a nonArchimedean analogue of the HodgeDconjecture – namely, the surjectivity of the boundary map in the localization sequence – in the case where the Abelian surface has good and ordinary reduction.Compositio Mathematica 04/2014; 150(4).  Compositio Mathematica 01/2014; 150(5).
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ABSTRACT: Generalizing previous results of DeligneSerre and Taylor, Galois representations are attached to cuspidal automorphic representations of unitary groups whose Archimedean component is a holomorphic limit of discrete series. The main ingredient is a construction of congruences, using the Hasse invariant, that is independent of qexpansions.Compositio Mathematica 01/2014; 150(2).  [Show abstract] [Hide abstract]
ABSTRACT: We explain how the AndréOort conjecture for a general Shimura variety can be deduced from the hyperbolic AxLindemann conjecture, a good lower bound for Galois orbits of special points and the definability, in the ominimal structure ℝ an , exp , of the restriction to a fundamental set of the uniformizing map of a Shimura variety. These ingredients are known in some important cases. As a consequence a proof of the AndréOort conjecture for projective special subvarieties of A 6 N for an arbitrary integer N is given.Compositio Mathematica 01/2014; 150(2).  Compositio Mathematica 01/2014; 150(6).
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ABSTRACT: In this paper, we construct a generalization of the Kohnen plus space for Hilbert modular forms of halfintegral weight. The Kohnen plus space can be characterized by the eigenspace of a certain Hecke operator. It can be also characterized by the behavior of the Fourier coefficients. For example, in the parallel weight case, a modular form of weight κ+(1/2) with ξth Fourier coefficient c(ξ) belongs to the Kohnen plus space if and only if c(ξ)=0 unless (1) κ ξ is congruent to a square modulo 4. The Kohnen subspace is isomorphic to a certain space of Jacobi forms. We also prove a generalization of the KohnenZagier formula.Compositio Mathematica 12/2013; 149(12).  [Show abstract] [Hide abstract]
ABSTRACT: The author extends a previous joint work with B. C. Ngô [J. Inst. Math. Jussieu 7, No. 1, 181–203 (2008; Zbl 1141.22005)] and gives a fixed point formula for the elliptic part of moduli spaces of Gshtukas with arbitrary modifications. The formula is similar to the fixed point formula of Kottwitz for certain Shimura varieties. The method is inspired by that of Kottwitz and simpler than that of Lafforgue for the fixed point formula of the moduli space of Drinfeld GL (r)shtukas.Compositio Mathematica 12/2013; 149(12). 
Article: Integral division points on curves
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ABSTRACT: Let k be a number field and S a set of primes containing all the infinite ones. Let A/k be a semiabelian variety, Γ 0 a finitely generated subgroup of A(k ¯) and Γ⊆A(k ¯) be the division group attached to Γ 0 , i.e the set of points P∈A(k ¯) such that there exists a integer n such that nP∈Γ 0 . If X/k is any variety and X ¯ its completion, define ∂X:=X ¯X. Let T be any subset of X ¯, and let T ¯ be its Zariski closure in X ¯. Any P∈X(k ¯) is said to be Sintegral relative to T if it is (T ¯∪∂X,S)integral on X ¯. The authors pose the following conjecture: Conjecture Let k and S be as above and let A/k be a semiabelian variety and Γ a division group in A(k ¯). Suppose that D is a nonzero effective divisor on A which is not the translate of any torsion divisor by any point of Γ. Then the set {P∈Γ:PisSintegralrelativetoD} is not Zariski dense in A. The authors then prove the conjecture for 1dimensional semiabelian varieties, i.e. for elliptic curves and 1dimensional tori.Compositio Mathematica 12/2013; 149(12).  [Show abstract] [Hide abstract]
ABSTRACT: Let $(X,B)$ be a projective log canonical pair such that $B$ is a $\Q$divisor, and that there is a surjective morphism $f\colon X\to Z$ onto a normal variety $Z$ satisfying: $K_X+B\sim_\Q f^*M$ for some $\Q$divisor $M$, and the augmented base locus ${\bf{B_+}}(M)$ does not contain the image of any log canonical centre of $(X,B)$. We will show that $(X,B)$ has a good log minimal model. An interesting special case is when $f$ is the identity morphism.Compositio Mathematica 05/2013;  [Show abstract] [Hide abstract]
ABSTRACT: Let K and F be complete discrete valuation fields of residue characteristic p>0. Let m be a positive integer no more than their absolute ramification indices. Let s and t be their uniformizers. Let L/K and E/F be finite extensions such that the modulo s^m of the extension O_L/O_K and modulo t^m of O_E/O_F are isomorphic. Let j=<m be a positive rational number. In this paper, we prove that the ramification of L/K is bounded by j if and only if the ramification of E/F is bounded by j. As an application, we prove that the categories of finite separable extensions of K and F whose ramifications are bounded by j are equivalent to each other, which generalizes a theorem of Deligne to the case of imperfect residue fields. We also show the compatibility of Scholl's theory of higher fields of norms with the ramification theory of AbbesSaito, and the integrality of small Artin and Swan conductors of abelian extensions of mixed characteristic.Compositio Mathematica 04/2013;  [Show abstract] [Hide abstract]
ABSTRACT: Schinzel's Hypothesis (H) was used by ColliotTh\'el\`ene and Sansuc, and later by Serre, SwinnertonDyer and others, to prove that the BrauerManin obstruction controls the Hasse principle and weak approximation on pencils of conics and similar varieties. We show that when the ground field is Q and the degenerate geometric fibres of the pencil are all defined over Q, one can use these methods to obtain unconditional results by replacing Hypothesis (H) with the finite complexity case of the generalised HardyLittlewood conjecture recently established by Green, Tao and Ziegler.Compositio Mathematica 04/2013;
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