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

„A quotient of the Lubin-Tate tower“
Dr. Judith Ludwig, Universität Bonn

In this talk we explain how to construct the quotient of an infinite-level Lubin-Tate space by the Borel subgroup $B(Q_p)$ of upper triangular matrices in $GL(2,Q_p)$ as a perfectoid space. The motivation for this is as follows. As I will review in my talk, Scholze recently constructed a candidate for the mod $p$ Jacquet-Langlands correspondence and the mod $p$ local Langlands correspondence for $GL(n,F)$, $F/Q_p$ finite. This candidate is given as the cohomology groups $H^i_{et}(P^{n-1},F_\pi), 0 \leq i \leq 2(n-1)$, where $F_\pi$ is a sheaf constructed from a smooth admissible representation $\pi$ of $GL(n,F)$. The finer properties of this candidate remain mysterious. As an application of the quotient construction one can show that in the case of $n=2,F=Q_p$, and $\pi$ an irreducible principal series representation or a twist of the Steinberg representation, the cohomology $H^i_{et}(P^{n-1},F_\pi)$ is concentrated in the middle degree.

Freitag, den 16. Dezember 2016 um 13:30 Uhr, in INF205, SR C Freitag, den 16. Dezember 2016 at 13:30, in INF205, SR C

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