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Séminaire de Géométrie Arithmétique Paris-Pékin-Tokyo

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

by Prof. A. TAMAGAWA (RIMS, University of Kyoto)

mercredi 13 avril 2016 de au (Europe/Paris)
at IHES ( Amphithéâtre Léon Motchane )
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).

Organisé par Ahmed Abbes
Contact Email: cecile@ihes.fr