On the Cohomology of Moduli of Mixed Characteristic Shtukas
Richard Magner (Boston University)
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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