Compositio Mathematica Journal Impact Factor & Information
Journal 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.
Current impact factor: 0.99
Impact Factor Rankings
2015 Impact Factor  Available summer 2016 

2014 Impact Factor  0.993 
2013 Impact Factor  1.043 
2012 Impact Factor  1.024 
2011 Impact Factor  1.187 
2010 Impact Factor  0.941 
2009 Impact Factor  1.246 
2008 Impact Factor  0.993 
2007 Impact Factor  0.882 
2006 Impact Factor  0.675 
2005 Impact Factor  0.758 
2004 Impact Factor  0.906 
2003 Impact Factor  0.662 
2002 Impact Factor  0.601 
2001 Impact Factor  0.447 
2000 Impact Factor  0.6 
1999 Impact Factor  0.639 
1998 Impact Factor  0.676 
1997 Impact Factor  0.463 
1996 Impact Factor  0.523 
1995 Impact Factor  0.47 
1994 Impact Factor  0.478 
1993 Impact Factor  0.463 
1992 Impact Factor  0.354 
Impact factor over time
Additional details
5year impact  1.23 

Cited halflife  >10.0 
Immediacy index  0.20 
Eigenfactor  0.01 
Article influence  2.38 
Website  Compositio Mathematica website 
Other titles  Compositio mathematica 
ISSN  0010437X 
OCLC  1564581 
Material type  Periodical, Internet resource 
Document type  Journal / Magazine / Newspaper, Internet Resource 
Publisher details
Foundation Compositio Mathematica
 Preprint
 Author can archive a preprint version
 Postprint
 Author can archive a postprint version
 Conditions
 On author's personal website, institutional website or electronic archive (including open access repository and arXiv)
 Publisher's version/PDF cannot be used
 Must update with publisher copyright and source must be acknowledged upon publication
 Must link to publisher version with DOI
 Statement regarding difference between preprint and published version
 Classification green
Publications in this journal
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ABSTRACT: Let $\mathbf{G}$ be the connected reductive group of type $E_{7,3}$ over $\mathbb{Q}$ and $\mathfrak{T}$ be the corresponding symmetric domain in $\mathbb{C}^{27}$ . Let ${\rm\Gamma}=\mathbf{G}(\mathbb{Z})$ be the arithmetic subgroup defined by Baily. In this paper, for any positive integer $k\geqslant 10$ , we will construct a (nonzero) holomorphic cusp form on $\mathfrak{T}$ of weight $2k$ with respect to ${\rm\Gamma}$ from a Hecke cusp form in $S_{2k8}(\text{SL}_{2}(\mathbb{Z}))$ . We follow Ikeda’s idea of using Siegel’s Eisenstein series, their Fourier–Jacobi expansions, and the compatible family of Eisenstein series.Compositio Mathematica 09/2015; DOI:10.1112/S0010437X15007538  [Show abstract] [Hide abstract]
ABSTRACT: We study ultrametric germs in one variable having an irrationally indifferent fixed point at the origin with a prescribed multiplier. We show that for many values of the multiplier, the cycles in the unit disk of the corresponding monic quadratic polynomial are ‘optimal’ in the following sense: they minimize the distance to the origin among cycles of the same minimal period of normalized germs having an irrationally indifferent fixed point at the origin with the same multiplier. We also give examples of multipliers for which the corresponding quadratic polynomial does not have optimal cycles. In those cases we exhibit a higherdegree polynomial such that all of its cycles are optimal. The proof of these results reveals a connection between the geometric location of periodic points of ultrametric power series and the lower ramification numbers of wildly ramified field automorphisms. We also give an extension of Sen’s theorem on wildly ramified field automorphisms, and a characterization of minimally ramified power series in terms of the iterative residue.Compositio Mathematica 09/2015; 1:136. DOI:10.1112/S0010437X15007575  [Show abstract] [Hide abstract]
ABSTRACT: With analytic applications in mind, in particular Beyond Endoscopy ([13]), we initiate the study of the elliptic part of the trace formula. Incorporating the approximate functional equation to the elliptic part we control the analytic behavior of the volumes of tori that appear in the elliptic part. Furthermore by carefully choosing the truncation parameter in the approximate functional equation we smoothout the singularities of orbital integrals. Finally by an application of Poisson summation we rewrite the elliptic part so that it is ready to be used in analytic applications, and in particular in Beyond Endoscopy. As a by product we also isolate the contributions of special representations as pointed out in [13].Compositio Mathematica 06/2015; DOI:10.1112/S0010437X15007320  [Show abstract] [Hide abstract]
ABSTRACT: In this article we explain how the results in [Bö2] allow one to attach a Hecke character to every cuspidal Drinfeld modular eigenform via its associated crystals constructed in [Bö1]. On the technical side, we prove along the way a number of results on endomorphism rings of τ sheaves and crystals. These are needed to exhibit the close relation between Hecke operators as endomorphisms of crystals on the one side and Frobenius automorphisms acting o etale sheaves associated to crystals on the other.Compositio Mathematica 06/2015; 1. DOI:10.1112/S0010437X15007290  [Show abstract] [Hide abstract]
ABSTRACT: We show that arithmetic local constants attached by Mazur and Rubin to pairs of selfdual Galois representations which are congruent modulo a prime number \$p>2\$ are compatible with the usual local constants at all primes not dividing \$p\$ and in two special cases also at primes dividing \$p\$. We deduce new cases of the \$p\$parity conjecture for Selmer groups of abelian varieties with real multiplication (Theorem 4.14) and elliptic curves (Theorem 5.10).Compositio Mathematica 04/2015; 1:121. DOI:10.1112/S0010437X14008069  [Show abstract] [Hide abstract]
ABSTRACT: Let $K$ be a totally real field. By the asymptotic Fermat's Last Theorem over $K$ we mean the statement that there is a constant $B_K$ such that for prime exponents $p>B_K$ the only solutions to the Fermat equation $a^p + b^p + c^p = 0$ with $a$, $b$, $c$ in $K$ are the trivial ones satisfying $abc = 0$. With the help of modularity, level lowering and image of inertia comparisons we give an algorithmically testable criterion which if satisfied by $K$ implies the asymptotic Fermat's Last Theorem over $K$. Using techniques from analytic number theory, we show that our criterion is satisfied by $K = \mathbb{Q}(\sqrt{d})$ for a subset of $d$ having density $5/6$ among the squarefree positive integers. We can improve this to density 1 if we assume a standard "EichlerShimura" conjecture.Compositio Mathematica 03/2015; 151:121. DOI:10.1112/S0010437X14007957  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we study the structure of the local components of the (shallow, i.e. without Up) Hecke algebras acting on the space of modular forms modulo p of level 1, and relate them to pseudodeformation rings. In many cases, we prove that those local components are regular complete local algebras of dimension 2, generalizing a recent result of Nicolas and Serre for the case p = 2.Compositio Mathematica 03/2015; 151(3):397415. DOI:10.1112/S0010437X1400774X  [Show abstract] [Hide abstract]
ABSTRACT: Let \$W\$ be an extended affine Weyl group. We prove that the minimal length elements \$w_{{\mathcal{O}}}\$ of any conjugacy class \${\mathcal{O}}\$ of \$W\$ satisfy some nice properties, generalizing results of Geck and Pfeiffer [On the irreducible characters of Hecke algebras, Adv. Math. 102 (1993), 79–94] on finite Weyl groups. We also study a special class of conjugacy classes, the straight conjugacy classes. These conjugacy classes are in a natural bijection with the Frobeniustwisted conjugacy classes of some \$p\$adic group and satisfy additional interesting properties. Furthermore, we discuss some applications to the affine Hecke algebra \$H\$. We prove that \$T_{w_{{\mathcal{O}}}}\$, where \${\mathcal{O}}\$ ranges over all the conjugacy classes of \$W\$, forms a basis of the cocenter \$H/[H,H]\$. We also introduce the class polynomials, which play a crucial role in the study of affine Deligne–Lusztig varieties He [Geometric and cohomological properties of affine Deligne–Lusztig varieties, Ann. of Math. (2) 179 (2014), 367–404].Compositio Mathematica 11/2014; 150(11). DOI:10.1112/S0010437X14007349  [Show abstract] [Hide abstract]
ABSTRACT: We apply results from both contact topology and exceptional surgery theory to study when Legendrian surgery on a knot yields a reducible manifold. As an application, we show that a reducible surgery on a noncabled positive knot of genus g must have slope 2g1, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum ThurstonBennequin numbers of cables.Compositio Mathematica 10/2014; DOI:10.1112/S0010437X15007599  Compositio Mathematica 09/2014; 150(09):14821484. DOI:10.1112/S0010437X14007489

Article: Random walks on projective spaces
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ABSTRACT: Let \$\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}G\$ be a connected real semisimple Lie group, \$V\$ be a finitedimensional representation of \$G\$ and \$\mu \$ be a probability measure on \$G\$ whose support spans a Zariskidense subgroup. We prove that the set of ergodic \$\mu \$stationary probability measures on the projective space \$\mathbb{P}(V)\$ is in onetoone correspondence with the set of compact \$G\$orbits in \$\mathbb{P}(V)\$. When \$V\$ is strongly irreducible, we prove the existence of limits for the empirical measures. We prove related results over local fields as the finiteness of the set of ergodic \$\mu \$stationary measures on the flag variety of \$G\$.Compositio Mathematica 09/2014; 150(09):15791606. DOI:10.1112/S0010437X1400726X  [Show abstract] [Hide abstract]
ABSTRACT: A technical ingredient in Faltings' original approach to padic comparison theorems involves the construction of $K(\pi, 1)$neighborhoods for a smooth scheme X over a mixed characteristic dvr with a perfect residue field: every point of X has an open neighborhood whose general fiber is a $K(\pi, 1)$ scheme (a notion analogous to having a contractible universal cover). We show how to extend this result to the logarithmically smooth case, which might help to simplify some proofs in padic Hodge theory. The main ingredient of the proof is a variant of a trick of Nagata used in his proof of the Noether Normalization Lemma.Compositio Mathematica 07/2014; 1. DOI:10.1112/S0010437X15007319  [Show abstract] [Hide abstract]
ABSTRACT: We classify all (abstract) homomorphisms from the group $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}{\sf PGL}_{r+1}(\mathbf{C})$ to the group ${\sf Bir}(M)$ of birational transformations of a complex projective variety $M$, provided that $r\geq \dim _\mathbf{C}(M)$. As a byproduct, we show that: (i) ${\sf Bir}(\mathbb{P}^n_\mathbf{C})$ is isomorphic, as an abstract group, to ${\sf Bir}(\mathbb{P}^m_\mathbf{C})$ if and only if $n=m$; and (ii) $M$ is rational if and only if ${\sf PGL}_{\dim (M)+1}(\mathbf{C})$ embeds as a subgroup of ${\sf Bir}(M)$.Compositio Mathematica 07/2014; 150(7). DOI:10.1112/S0010437X13007835  [Show abstract] [Hide abstract]
ABSTRACT: We introduce support varieties for rational representations of a linear algebraic group $G$ of exponential type over an algebraically closed field $k$ of characteristic $p > 0$. These varieties are closed subspaces of the space $V(G)$ of all 1parameter subgroups of $G$. The functor $M \mapsto V(G)_M$ satisfies many of the standard properties of support varieties satisfied by finite groups and other finite group schemes. Furthermore, there is a close relationship between $V(G)_M$ and the family of support varieties $V_r(G)_M$ obtained by restricting the $G$ action to Frobenius kernels $G_{(r)} \subset G$. These support varieties seem particularly appropriate for the investigation of infinite dimensional rational $G$modules.Compositio Mathematica 06/2014; 151(04). DOI:10.1112/S0010437X14007726
Data provided are for informational purposes only. Although carefully collected, accuracy cannot be guaranteed. The impact factor represents a rough estimation of the journal's impact factor and does not reflect the actual current impact factor. Publisher conditions are provided by RoMEO. Differing provisions from the publisher's actual policy or licence agreement may be applicable.