Session S21 - Galois representations and automorphic forms

Tuesday, July 13, 13:40 ~ 14:20 UTC-3

Poincare duality for modular representations of $p$-adic groups and Hecke algebras

Karol Koziol

University of Michigan, United States   -   This email address is being protected from spambots. You need JavaScript enabled to view it.

The mod-$p$ representations theory of $p$-adic reductive groups (such as $\textrm{GL}_2(\mathbb{Q}_p)$) is one of the foundations of the rapidly developing mod-$p$ local Langlands program. However, many constructions from the case of complex coefficients are quite poorly behaved in the mod-$p$ setting, and it becomes necessary to use derived functors. In this talk, I'll describe how this situation looks for the functor of smooth duality on mod-$p$ representations, and discuss the construction of a Poincare duality spectral sequence relating Kohlhaase's functors of higher smooth duals with modules over the (pro-$p$) Iwahori-Hecke algebra.

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