# Compositio Mathematica (COMPOS MATH)

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.

## Journal Impact: 1.26*

*This value is calculated using ResearchGate data and is based on average citation counts from work published in this journal. The data used in the calculation may not be exhaustive.

## Journal impact history

2017 Journal impact Available summer 2018 1.26 1.07 1.38 0.90 1.25 0.73 0.89 0.74 1.57 1.56 1.06 1.00 1.17 1.00 0.81 0.97

## Journal impact over time

Journal impact
.
Year

Cited half-life >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

This journal may support self-archiving.

## Publications in this journal

• ##### Article: Level structures on abelian varieties and Vojta’s conjecture
[Hide abstract] ABSTRACT: Assuming Vojta’s conjecture, and building on recent work of the authors, we prove that, for a fixed number field $K$ and a positive integer $g$ , there is an integer $m_{0}$ such that for any $m>m_{0}$ there is no principally polarized abelian variety $A/K$ of dimension $g$ with full level- $m$ structure. To this end, we develop a version of Vojta’s conjecture for Deligne–Mumford stacks, which we deduce from Vojta’s conjecture for schemes.
Article · Feb 2017 · Compositio Mathematica
• ##### Article: Refined global Gan–Gross–Prasad conjecture for Fourier–Jacobi periods on symplectic groups
[Hide abstract] ABSTRACT: In this paper, we propose a conjectural identity between the Fourier–Jacobi periods on symplectic groups and the central value of certain Rankin–Selberg $L$ -functions. This identity can be viewed as a refinement to the global Gan–Gross–Prasad conjecture for $\text{Sp}(2n)\times \text{Mp}(2m)$ . To support this conjectural identity, we show that when $n=m$ and $n=m\pm 1$ , it can be deduced from the Ichino–Ikeda conjecture in some cases via theta correspondences. As a corollary, the conjectural identity holds when $n=m=1$ or when $n=2$ , $m=1$ and the automorphic representation on the bigger group is endoscopic.
Article · Jan 2017 · Compositio Mathematica
• ##### Article: Corrigendum: Connected components of affine Deligne–Lusztig varieties in mixed characteristic
[Hide abstract] ABSTRACT: We correct an error in our paper ‘Connected components of affine Deligne–Lusztig varieties in mixed characteristic’.
Article · Jan 2017 · Compositio Mathematica
• ##### Article: Corrigendum: Analytic representation theory of Lie groups: general theory and analytic globalizations of Harish-Chandra modules
[Hide abstract] ABSTRACT: We correct the proof of the main result of the paper, Theorem 5.7. Our corrected proof relies on weaker versions of a number of intermediate results from the paper. The original, more general, versions of these statements are not known to be true.
Article · Jan 2017 · Compositio Mathematica
• ##### Article: Paraboline variation over -adic families of -modules
[Hide abstract] ABSTRACT: We study the $p$ -adic variation of triangulations over $p$ -adic families of $(\unicode[STIX]{x1D711},\unicode[STIX]{x1D6E4})$ -modules. In particular, we study certain canonical sub-filtrations of the pointwise triangulations and show that they extend to affinoid neighborhoods of crystalline points. This generalizes results of Kedlaya, Pottharst and Xiao and (independently) Liu in the case where one expects the entire triangulation to extend. We also study the ramification of weight parameters over natural $p$ -adic families.
Article · Jan 2017 · Compositio Mathematica
• ##### Article: Ramification conjecture and Hirzebruch’s property of line arrangements
[Hide abstract] ABSTRACT: The ramification of a polyhedral space is defined as the metric completion of the universal cover of its regular locus. We consider mainly polyhedral spaces of two origins: quotients of Euclidean space by a discrete group of isometries and polyhedral metrics on $\mathbb{C}\text{P}^{2}$ with singularities at a collection of complex lines. In the former case we conjecture that quotient spaces always have a $\text{CAT}[0]$ ramification and prove this in several cases. In the latter case we prove that the ramification is $\text{CAT}[0]$ if the metric on $\mathbb{C}\text{P}^{2}$ is non-negatively curved. We deduce that complex line arrangements in $\mathbb{C}\text{P}^{2}$ studied by Hirzebruch have aspherical complement.
Article · Oct 2016 · Compositio Mathematica
• ##### Article: Gonality of abstract modular curves in positive characteristic:
[Hide abstract] ABSTRACT: Let $C$ be a smooth, separated and geometrically connected curve over a finitely generated field $k$ of characteristic $p\geqslant 0$ , ${\it\eta}$ the generic point of $C$ and ${\it\pi}_{1}(C)$ its étale fundamental group. Let $f:X\rightarrow C$ be a smooth proper morphism, and $i\geqslant 0$ , $j$ integers. To the family of continuous $\mathbb{F}_{\ell }$ -linear representations ${\it\pi}_{1}(C)\rightarrow \text{GL}(R^{i}f_{\ast }\mathbb{F}_{\ell }(j)_{\overline{{\it\eta}}})$ (where $\ell$ runs over primes $\neq p$ ), one can attach families of abstract modular curves $C_{0}(\ell )$ and $C_{1}(\ell )$ , which, in this setting, are the analogues of the usual modular curves $Y_{0}(\ell )$ and $Y_{1}(\ell )$ . If $i\not =2j$ , it is conjectured that the geometric and arithmetic gonalities of these abstract modular curves go to infinity with $\ell$ (for the geometric gonality, under a certain necessary condition). We prove the conjecture for the arithmetic gonality of the abstract modular curves $C_{1}(\ell )$ . We also obtain partial results for the growth of the geometric gonality of $C_{0}(\ell )$ and $C_{1}(\ell )$ . The common strategy underlying these results consists in reducing by specialization theory to the case where the base field $k$ is finite in order to apply techniques of counting rational points.
Article · Jul 2016 · Compositio Mathematica
• ##### Article: Quivers with loops and generalized crystals
[Hide abstract] ABSTRACT: In the context of varieties of representations of arbitrary quivers, possibly carrying loops, we define a generalization of Lusztig Lagrangian subvarieties. From the combinatorial study of their irreducible components arises a structure richer than the usual Kashiwara crystals. Along with the geometric study of Nakajima quiver varieties, in the same context, this yields a notion of generalized crystals, coming with a tensor product. As an application, we define the semicanonical basis of the Hopf algebra generalizing quantum groups, which was already equipped with a canonical basis. The irreducible components of the Nakajima varieties provide the family of highest weight crystals associated to dominant weights, as in the classical case.
Article · Jul 2016 · Compositio Mathematica
• ##### Article: Motivic cohomology spectral sequence and Steenrod operations
[Hide abstract] ABSTRACT: For a prime number $p$ , we show that differentials $d_{n}$ in the motivic cohomology spectral sequence with $p$ -local coefficients vanish unless $p-1$ divides $n-1$ . We obtain an explicit formula for the first non-trivial differential $d_{p}$ , expressing it in terms of motivic Steenrod $p$ -power operations and Bockstein maps. To this end, we compute the algebra of operations of weight $p-1$ with $p$ -local coefficients. Finally, we construct examples of varieties having non-trivial differentials $d_{p}$ in their motivic cohomology spectral sequences.
Article · Jun 2016 · Compositio Mathematica
• ##### Article: A remark on fullness of some group measure space von Neumann algebras
[Hide abstract] ABSTRACT: Recently C. Houdayer and Y. Isono have proved among other things that every biexact group $\Gamma$ has the property that for any non-singular strongly ergodic action $\Gamma\curvearrowright (X,\mu)$ on a standard measure space the group measure space von Neumann algebra $\Gamma\ltimes L^\infty(X)$ is full. In this note, we prove the same property for a wider class of groups, notably including $\mathrm{SL}(3,{\mathbb Z})$. We also prove that for any connected simple Lie group $G$ with finite center, any lattice $\Gamma\le G$, and any closed non-amenable subgroup $H\le G$, the non-singular action $\Gamma\curvearrowright G/H$ is strongly ergodic and the von Neumann factor $\Gamma\ltimes L^\infty(G/H)$ is full.
Article · Feb 2016 · Compositio Mathematica
• ##### Article: Real-dihedral harmonic Maass forms and CM-values of Hilbert modular functions
[Hide abstract] ABSTRACT: In this paper, we study real-dihedral harmonic Maass forms and their Fourier coefficients. The main result expresses the values of Hilbert modular forms at twisted CM 0-cycles in terms of these Fourier coefficients. This is a twisted version of the main theorem in Bruinier and Yang [ CM-values of Hilbert modular functions , Invent. Math. 163 (2006), 229–288] and provides evidence that the individual Fourier coefficients are logarithms of algebraic numbers in the appropriate real-quadratic field. From this result and numerical calculations, we formulate an algebraicity conjecture, which is an analogue of Stark’s conjecture in the setting of harmonic Maass forms. Also, we give a conjectural description of the primes appearing in CM-values of Hilbert modular functions.
Article · Feb 2016 · Compositio Mathematica
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##### Article: Non-rigid quartic -folds
[Hide abstract] ABSTRACT: Let $X\subset \mathbb{P}^{4}$ be a terminal factorial quartic $3$ -fold. If $X$ is non-singular, $X$ is birationally rigid , i.e. the classical minimal model program on any terminal $\mathbb{Q}$ -factorial projective variety $Z$ birational to $X$ always terminates with $X$ . This no longer holds when $X$ is singular, but very few examples of non-rigid factorial quartics are known. In this article, we first bound the local analytic type of singularities that may occur on a terminal factorial quartic hypersurface $X\subset \mathbb{P}^{4}$ . A singular point on such a hypersurface is of type $cA_{n}$ ( $n\geqslant 1$ ), or of type $cD_{m}$ ( $m\geqslant 4$ ) or of type $cE_{6},cE_{7}$ or $cE_{8}$ . We first show that if $(P\in X)$ is of type $cA_{n}$ , $n$ is at most $7$ and, if $(P\in X)$ is of type $cD_{m}$ , $m$ is at most $8$ . We then construct examples of non-rigid factorial quartic hypersurfaces whose singular loci consist (a) of a single point of type $cA_{n}$ for $2\leqslant n\leqslant 7$ , (b) of a single point of type $cD_{m}$ for $m=4$ or $5$ and (c) of a single point of type $cE_{k}$ for $k=6,7$ or $8$ .
Full-text available · Article · Dec 2015 · Compositio Mathematica
• ##### Article: A higher dimensional generalization of Lichtenbaum duality in terms of the Albanese map
[Hide abstract] ABSTRACT: We present a conjectural formula describing the cokernel of the Albanese map of zero-cycles of smooth projective varieties $X$ over $p$-adic fields in terms of the N\'eron-Severi group and provide a proof under additional assumptions on an integral model of $X$. The proof depends on a non-degeneracy result of Brauer-Manin pairing due to Saito-Sato and on Gabber-de Jong's comparison result of cohomological- and Azumaya-Brauer groups. We can consider the local-global problem of the Albanese-cokernel; the abelian group on the "local side" turns out to be a finite group.
Article · Dec 2015 · Compositio Mathematica
• ##### Article: The extremal Secant Conjecture for curves of arbitrary gonality
[Hide abstract] ABSTRACT: Let $C$ be a curve and $L$ a very ample line bundle. The Green-Lazarsfeld Secant conjecture predicts that if the degree of $L$ is at least $2g+p+1-2h^1(C,L)-Cliff(C)$ and if, in addition, $L$ is $p+1$ very ample, then the Koszul group $K_{p,2}(C,L)$ vanishes. In this article, we establish the conjecture in the extremal case, i.e.\ the case where the degree is exactly $2g+p+1-2h^1(C,L)-Cliff(C)$, subject to explicit genericity assumptions on $C$ and $L$. In particular, the gonality of $C$ is allowed to be arbitrary (in our cases $gon(C)=Cliff(C)+2$).
Article · Dec 2015 · Compositio Mathematica
• ##### Article: On Berman-Gibbs stability and K-stability of ℚ-Fano varieties
[Hide abstract] ABSTRACT: The notion of Berman-Gibbs stability was originally introduced by Robert Berman for $\mathbb{Q}$-Fano varieties $X$. We show that the pair $(X, -K_X)$ is K-stable (resp. K-semistable) provided that $X$ is Berman-Gibbs stable (resp. semistable).
Article · Nov 2015 · Compositio Mathematica
• ##### Article: The pro--Iwahori Hecke algebra of a reductive -adic group I
[Hide abstract] ABSTRACT: Let $R$ be a commutative ring, let $F$ be a locally compact non-archimedean field of finite residual field $k$ of characteristic $p$ , and let $\mathbf{G}$ be a connected reductive $F$ -group. We show that the pro- $p$ -Iwahori Hecke $R$ -algebra of $G=\mathbf{G}(F)$ admits a presentation similar to the Iwahori–Matsumoto presentation of the Iwahori Hecke algebra of a Chevalley group, and alcove walk bases satisfying Bernstein relations. This was previously known only for a $F$ -split group $\mathbf{G}$ .
Article · Oct 2015 · Compositio Mathematica
• ##### Article: Rational Points on Erdos-Selfridge Superelliptic Curves
[Hide abstract] ABSTRACT: Given $k \geq 2$, we show that there are at most finitely many rational numbers $x$ and $y \neq 0$ and integers $\ell \geq 2$ (with $(k,\ell) \neq (2,2)$) for which $$x (x+1) \cdots (x+k-1) = y^\ell.$$ In particular, if we assume that $\ell$ is prime, then all such triples $(x,y,\ell)$ satisfy either $y=0$ or $\log \ell < 3^k$.
Article · Oct 2015 · Compositio Mathematica