# Compositio Mathematica Journal Impact Factor & Information

Publisher: London Mathematical Society, Foundation Compositio Mathematica

## 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.

## Impact Factor Rankings

2015 Impact Factor Available summer 2016 0.993 1.043 1.024 1.187 0.941 1.246 0.993 0.882 0.675 0.758 0.906 0.662 0.601 0.447 0.6 0.639 0.676 0.463 0.523 0.47 0.478 0.463 0.354

## Impact factor over time

Impact factor
.
Year

5-year impact 1.23 >10.0 0.20 0.01 2.38 Compositio Mathematica website Compositio mathematica 0010-437X 1564581 Periodical, Internet resource Journal / Magazine / Newspaper, Internet Resource

## Publisher details

• Pre-print
• Author can archive a pre-print version
• Post-print
• Author can archive a post-print 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 pre-print and published version
• Classification
​ green

## Publications in this journal

• ##### Article: Cusp forms on the exceptional group of type
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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 (non-zero) holomorphic cusp form on $\mathfrak{T}$ of weight $2k$ with respect to ${\rm\Gamma}$ from a Hecke cusp form in $S_{2k-8}(\text{SL}_{2}(\mathbb{Z}))$ . 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
• ##### Article: Optimal cycles in ultrametric dynamics and minimally ramified power series
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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 higher-degree 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; -1:1-36. DOI:10.1112/S0010437X15007575
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##### Article: Beyond Endoscopy via the Trace Formula-I: Poisson Summation and Contributions of Special Representations
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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 smooth-out 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
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##### Article: Hecke characters associated to Drinfeld modular forms
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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
• ##### Article: Compatibility of arithmetic and algebraic local constants (the case )
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ABSTRACT: We show that arithmetic local constants attached by Mazur and Rubin to pairs of self-dual 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; -1:1-21. DOI:10.1112/S0010437X14008069
• ##### Article: The Asymptotic Fermat's Last Theorem for Five-Sixths of Real Quadratic Fields
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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 "Eichler-Shimura" conjecture.
Compositio Mathematica 03/2015; 151:1-21. DOI:10.1112/S0010437X14007957
• ##### Article: Level 1 Hecke algebras of modular forms modulo
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ABSTRACT: In this paper, we study the structure of the local components of the (shallow, i.e. without U-p) Hecke algebras acting on the space of modular forms modulo p of level 1, and relate them to pseudo-deformation 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):397-415. DOI:10.1112/S0010437X1400774X
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##### Article: Minimal length elements of extended affine Weyl groups
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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 Frobenius-twisted 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
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##### Article: Contact structures and reducible surgeries
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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 non-cabled positive knot of genus g must have slope 2g-1, leading to a proof of the cabling conjecture for positive knots of genus 2. Our techniques also produce bounds on the maximum Thurston-Bennequin numbers of cables.
Compositio Mathematica 10/2014; DOI:10.1112/S0010437X15007599
• ##### Article: Corrigendum: Filtering free resolutions
Compositio Mathematica 09/2014; 150(09):1482-1484. 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 finite-dimensional representation of \$G\$ and \$\mu \$ be a probability measure on \$G\$ whose support spans a Zariski-dense subgroup. We prove that the set of ergodic \$\mu \$-stationary probability measures on the projective space \$\mathbb{P}(V)\$ is in one-to-one 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):1579-1606. DOI:10.1112/S0010437X1400726X
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##### Article: $K(\pi, 1)$-neighborhoods and comparison theorems
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ABSTRACT: A technical ingredient in Faltings' original approach to p-adic 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 p-adic 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
• ##### Article: Morphisms between Cremona groups and characterization of rational varieties
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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
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##### Article: Support varieties for rational representations
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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 1-parameter 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