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#### Seminar der Forschergruppe 'Symmetrie, Geometrie und Arithmetik'

„A mod $p$ local Langlands type correspondence for $p$-adic ${\rm GL}_n$'s“
Prof. Dr. Elmar Große-Klönne, Humboldt-Universität zu Berlin

Let $F$ be a finite extension of ${\mathbb Q}_p$, let $n\in{\mathbb N}$, let $k$ be a (sufficiently large) field of characteristic $p$. Put $G={\rm GL}_n(F)$. Ideally, an (as yet hypothetical) mod $p$-local Langlands correspondence should relate (suitable) admissible smooth $G$-representations over $k$ with $n$-dimensional ${\rm Gal}(\overline{F}/F)$-representations over $k$. As an approximation, we construct a similar correspondence with $G$-representations replaced by modules over the pro-$p$-Iwahori-Hecke algebra $H$ (over $k$) of $G$. An entirely new feature (e.g. when compared with more traditional Langlands type correspondences) is that this correspondence is even induced by an exact functor of abelian categories which is fully faithful on supersingular $H$-modules.

Freitag, den 30. Juni 2017 um 13:30 Uhr, in INF205, SR A Freitag, den 30. Juni 2017 at 13:30, in INF205, SR A

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Dr. Otmar Venjakob