On the p-adic theory of local models II

Abstract: This second talk (based on joint work with Anschütz–Gleason–Richarz) concerns the Scholze–Weinstein conjecture on the representability of v-sheaf local models for geometric conjugacy classes of minuscule coweights. I'll start by reviewing previously known instances of local models in PEL cases by Rapoport–Zink, and also via power series Grassmannians by Pappas–Zhu. I'll briefly explain how to slightly refine the latter (joint with Fakhruddin–Haines–Richarz). Building on this, I'll explain the comparison of p-adic admissible loci in the Witt Grassmannian with those found in power series Grassmannians. Next, I'll prove the specialization principle for sufficiently nice kimberlites, which include v-sheaf local models (even for non-minuscule cocharacters). Finally, I'm going to explain how to compute the specialization mapping in families, deducing the Scholze–Weinstein conjecture.

commutative algebraalgebraic geometrynumber theory

Audience: researchers in the topic

Recent Advances in Modern p-Adic Geometry (RAMpAGe)

Series comments: The Zoom Meeting ID is: 995 3670 1681. The password for the series is: *The first three-digit prime*. Please visit the external homepage for notes and videos from past talks.