La monodromie Hamiltonienne des cycles évanescents

Meromorphic nearby cycle functors and monodromies of meromorphic functions (with Appendix by T. Saito)

We introduce meromorphic nearby cycle functors and study their functorial properties. Moreover we apply them to monodromies of meromorphic functions in various situations. Combinatorial descriptions of their reduced Hodge spectra and Jordan normal forms will be obtained.

Monodromie algebrique des groupes d'Artin diedraux

Towards the study of the representation theory of any dihedral Artin group B, we build rational morphisms from B to the group of invertible elements of the associated infinitesimal braids algebra. For this we build analogues of Drinfeld associators, in rank 2 for arbitrary dihedral symmetries of the plane.

阿贝尔簇的有限单值群

Groupes de monodromie finie des variétés abéliennes

本文研究数域上阿贝尔簇的有限单值群，给出有限群可实现为给定维度有限单值群的判据，并应用于半稳定度，得到格罗滕迪克半稳定约化定理的有效版本。

Correspondance locale de Langlands et monodromie des espaces de Drinfeld

The conjecture stated by Carayol in [{\em Non-abelian Lubin-Tate theory.} Automorphic forms, Shimura varieties and $L$-functions, vol II: 15--39, Academic Press,1990] predicted that the {\em supercuspidal part} of the l-adic cohomology of the moduli spaces classifying certain formal groups introduced by Drinfeld would provide a simultaneaous "realization" of Langlands and Jacquet-Langlands local correspondences for {\em supercuspidal} representations of $GL_d$. By works of Harris, Boyer, Harris-Taylor and Hausberger, this conjecture is now proved. On another hand, recent works by Boyer and Fal…

La $\mathrm{Z}_l$-cohomologie du modèle de Deligne-Carayol est sans torsion

This article is the $\mathrm{Z}_l$-version of my paper "Monodromie du faisceau pervers des cycles évanescents de quelques variétés de Shimura simples" in Invent. Math. 2009 vol 177 pp. 239-280, where we study the vanishing cycles of some unitary Shimura variety. The aim is to prove that the cohomology sheaves of this complexe are free so that, thanks to the main theorem of Berkovich on vanishing cycles, we can deduce that the $\mathrm{Z}_l$-cohomology of the model of Deligne-Carayol is free. There will be a second article which will be the $\mathrm{Z}_l$ version of my paper "Conjecture de mono…

Coxeter elements for vanishing cycles of type $A_{1/2\infty}$ and $D_{1/2\infty}$

We introduce two entire functions $f_{A_{1/2\infty}}$and $f_{D_{1/2\infty}}$ in two variables. Both of them have only two critical values 0 and 1, and the associated maps $\C^2 to \C$ define topologically locally trivial fibrations over $\C\setminus{0,1\}$. All critical points are ordinary double points, and the associated vanishing cycles span the middle homology group of the general fiber, whose intersection diagram forms bi-partitely decomposed quivers of type $A_{1/2\infty}$ and $D_{1/2\infty}$, respectively. Coxeter elements of type $A_{1/2\infty}$ and $D_{1/2\infty}$, acting on the middl…