# Compositio Mathematica (COMPOS MATH)

## 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

2016 Impact Factor | Available summer 2017 |
---|---|

2014 / 2015 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

5-year impact | 1.23 |
---|---|

Cited half-life | >10.0 |

Immediacy index | 0.20 |

Eigenfactor | 0.01 |

Article influence | 2.38 |

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 |

## Publisher details

Foundation Compositio Mathematica

- 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

- Classificationgreen

## Publications in this journal

- [Show abstract] [Hide abstract]

**ABSTRACT:**This paper is about the reduced group $C^{\ast }$ -algebras of real reductive groups, and about Hilbert $C^{\ast }$ -modules over these $C^{\ast }$ -algebras. We shall do three things. First, we shall apply theorems from the tempered representation theory of reductive groups to determine the structure of the reduced $C^{\ast }$ -algebra (the result has been known for some time, but it is difficult to assemble a full treatment from the existing literature). Second, we shall use the structure of the reduced $C^{\ast }$ -algebra to determine the structure of the Hilbert $C^{\ast }$ -bimodule that represents the functor of parabolic induction. Third, we shall prove that the parabolic induction bimodule admits a secondary inner product, using which we can define a functor of parabolic restriction in tempered representation theory. We shall prove in a sequel to this paper that parabolic restriction is adjoint, on both the left and the right, to parabolic induction in the context of tempered unitary Hilbert space representations. - [Show abstract] [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: Non-rigid quartic -folds

[Show abstract] [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 $8$ . - [Show abstract] [Hide abstract]

**ABSTRACT:**The notion of Berman–Gibbs stability was originally introduced by Berman for $\mathbb{Q}$ -Fano varieties $X$ . We show that the pair $(X,-K_{X})$ is K-stable (respectively K-semistable) provided that $X$ is Berman–Gibbs stable (respectively semistable). - [Show abstract] [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 $\mathbf{G}$ . - [Show abstract] [Hide abstract]

**ABSTRACT:**In this paper we establish a Chowla–Selberg formula for abelian CM fields. This is an identity which relates values of a Hilbert modular function at CM points to values of Euler’s gamma function ${\rm\Gamma}$ and an analogous function ${\rm\Gamma}_{2}$ at rational numbers. We combine this identity with work of Colmez to relate the CM values of the Hilbert modular function to Faltings heights of CM abelian varieties. We also give explicit formulas for products of exponentials of Faltings heights, allowing us to study some of their arithmetic properties using the Lang–Rohrlich conjecture. - [Show abstract] [Hide abstract]

**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. - [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 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. - [Show abstract] [Hide abstract]

**ABSTRACT:**Under endoscopic assumptions about L-packets of unitary groups, we prove the local Gan Gross Prasad conjecture for tempered representations of unitary groups over padic fields. Roughly, this conjecture says that branching laws for U (n 1) c U (n) can be computed using epsilon factors. - [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 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]. - [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. - [Show abstract] [Hide abstract]

**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). - [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 "Eichler-Shimura" conjecture. - [Show abstract] [Hide abstract]

**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. - [Show abstract] [Hide abstract]

**ABSTRACT:**We study a Hermitian form \$h\$ over a quaternion division algebra \$Q\$ over a field (\$h\$ is supposed to be alternating if the characteristic of the field is two). For generic \$h\$ and \$Q\$, for any integer \$i\in [1,\;n/2]\$, where \$n:=\dim _{Q}h\$, we show that the variety of \$i\$-dimensional (over \$Q\$) totally isotropic right subspaces of \$h\$ is \$2\$-incompressible. The proof is based on a computation of the Chow ring for the classifying space of a certain parabolic subgroup in a split simple adjoint affine algebraic group of type \$C_{n}\$. As an application, we determine the smallest value of the \$J\$-invariant of a non-degenerate quadratic form divisible by a \$2\$-fold Pfister form; we also determine the biggest values of the canonical dimensions of the orthogonal Grassmannians associated to such quadratic forms. - [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 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].

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.