Laboratoire Alexander Grothendieck, Institut des Hautes Études Scientifiques,
Morningside Center of Mathematics, Chinese Academy of Sciences,
Département des Sciences Mathématiques de l'Université de Tokyo

Ahmed Abbes (CNRS, IHÉS), Fabrice Orgogozo (CNRS, École polytechnique), Takeshi Saito (Université de Tokyo),
Atsushi Shiho (Université de Tokyo), Ye Tian (Morningside Center for Mathematics),
Takeshi Tsuji (Université de Tokyo), Weizhe Zheng (Morningside Center for Mathematics)

Mercredi 13 avril 2016 de 10h30 à 11h30 (exceptionnellement à l'amphi Motchane)

A. Tamagawa (RIMS, University of Kyoto)

Semisimplicity of geometric monodromy on étale cohomology (joint work with Anna Cadoret and Chun Yin Hui)

Let K be a function field over an algebraically closed field of characteritic p \geq 0, X a proper smooth K-scheme, and l a prime distinct from p. Deligne proved that the Q_l-coefficient étale cohomology groups of the geometric fiber of X--> K are always semisimple as G_K-modules. In this talk, we consider a similar problem for the F_l-coefficient étale cohomology groups. Among other things, we show that if p=0 (resp. in general), they are semisimple for all but finitely many l's (resp. for all l's in a set of density 1).