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SUMMARY:Semisimplicity of certain Galois representations occurring in etal
 e cohomology of unitary Shimura varieties - Jan Nekovář (Sorbonne Univer
 sité)
DTSTART:20180605T133000Z
DTEND:20180605T143000Z
UID:TALK105415@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:Conjecturally\, the category of pure motives over a finitely g
 enerated field k should be semisimple. Consequently\, l-adic étale cohomo
 logy of a smooth projective variety over k should be a semisimple represen
 tation of the absolute Galois group of k. This was proved by Faltings for 
 H1\, as a consequence of his proof of Tate's conjecture. In this talk\, wh
 ich is based on a joint work with K. Fayad\, I am going to explain a proof
  of the semisimplicity of the Galois action on a certain part of étale co
 homology of unitary Shimura varieties. The most satisfactory result is obt
 ained for unitary groups of signature (n\,0) × (n-1\,1) × (1\,n-1) × (0
 \,n).
LOCATION:MR13
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