## View abstract

### 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. document.getElementById('cloak05124a8467bc64af439b6cd2d4f70678').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy05124a8467bc64af439b6cd2d4f70678 = 'kk&#111;z&#105;&#111;l' + '&#64;'; addy05124a8467bc64af439b6cd2d4f70678 = addy05124a8467bc64af439b6cd2d4f70678 + '&#117;m&#105;ch' + '&#46;' + '&#101;d&#117;'; var addy_text05124a8467bc64af439b6cd2d4f70678 = 'kk&#111;z&#105;&#111;l' + '&#64;' + '&#117;m&#105;ch' + '&#46;' + '&#101;d&#117;';document.getElementById('cloak05124a8467bc64af439b6cd2d4f70678').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy05124a8467bc64af439b6cd2d4f70678 + '\'>'+addy_text05124a8467bc64af439b6cd2d4f70678+'<\/a>';

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.