On the Cohomology of Moduli of Mixed Characteristic Shtukas

Richard Magner (Boston University)

13-Aug-2020, 16:00-17:20 (4 years ago)

Abstract: We review mixed characteristic shtukas and their moduli. These generalize the Lubin-Tate tower and other Rapoport-Zink spaces. Under the Kottwitz conjecture, the cohomology of these spaces are expected to realize the local Langlands correspondence. The data defining these spaces involve cocharacters of a Lie group; when the cocharacter is minuscule, we recover classical Rapoport-Zink spaces. In the case of $\mathrm{GL}_n$, we show that the Kottwitz conjecture for general cocharacters can be reduced to the minuscule case. This depends on a geometric Satake equivalence for the $B_{\mathrm{dR}}$-affine Grassmanian, due to Fargues and Scholze, and a formula of Imai on cohomology derived from it.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic


Recent Advances in Modern p-Adic Geometry (RAMpAGe)

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