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On the cohomology of local Shimura varieties

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Peter Scholze
U Bonn
Mon, 2016-06-06 09:30 - 10:30
MPIM Lecture Hall

Let $G$ be a reductive group over $Q_p$. Fargues conjectured a geometric Langlands type statement
for the stack Bun_G of $G$-bundles on the Fargues-Fontaine curve, refining the conjectural local
Langlands correspondence. The conjecture requires a formalism of "constructible" $l$-adic sheaves
on Bun_G, and a geometric Satake equivalence for the B_dR-Grassmannian. We will explain some
progress towards establishing such a formalism. If time permits, we will indicate some expected
applications of the formalism to open problems in the area.


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