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

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

mercredi 13 avr. 2016, 10:30 → 11:30 Europe/Paris

Amphithéâtre Léon Motchane (IHES)

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).