Semisimplicity of certain Galois representations occurring in etale cohomology of unitary Shimura varieties

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• Jan Nekovář (Sorbonne Université)
• Tuesday 05 June 2018, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jack Thorne.

Conjecturally, the category of pure motives over a finitely generated field k should be semisimple. Consequently, l-adic étale cohomology of a smooth projective variety over k should be a semisimple representation 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, which 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 cohomology of unitary Shimura varieties. The most satisfactory result is obtained for unitary groups of signature (n,0) × (n-1,1) × (1,n-1) × (0,n).

This talk is part of the Number Theory Seminar series.

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