Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo
# Semisimplicity of geometric monodromy on étale cohomology (joint work with Anna Cadoret and Chun Yin Hui)

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Amphithéâtre Léon Motchane (IHES)
### Amphithéâtre Léon Motchane

#### IHES

Le Bois Marie
35, route de Chartres
91440 Bures-sur-Yvette

Description

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).

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