On integral local Shimura varieties
Georgios Pappas, Michael Rapoport

TL;DR
This paper constructs integral local Shimura varieties as formal schemes generalizing known models, proves Scholze's conjecture for a broad class of cases, and relates these schemes to local Shimura varieties.
Contribution
It provides a new construction of integral local Shimura varieties for all classical groups at odd p and proves Scholze's conjecture in abelian type cases for p ≠ 2.
Findings
Construction of integral local Shimura varieties for classical groups.
Proof of Scholze's conjecture for abelian type cases when p ≠ 2.
Relation established between the formal schemes and local Shimura varieties.
Abstract
We give a construction of "integral local Shimura varieties" which are formal schemes that generalize the well-known integral models of the Drinfeld -adic upper half spaces. The construction applies to all classical groups, at least for odd . These formal schemes also generalize the formal schemes defined by Rapoport-Zink via moduli of -divisible groups, and are characterized purely in group-theoretic terms. More precisely, for a local -adic Shimura datum and a quasi-parahoric group scheme for , Scholze has defined a functor on perfectoid spaces which parametrizes -adic shtukas. He conjectured that this functor is representable by a normal formal scheme which is locally formally of finite type and flat over . Scholze-Weinstein proved this conjecture when is of (P)EL type by using Rapoport-Zink formal schemes. We…
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Taxonomy
TopicsAdvanced Algebra and Geometry · Algebraic Geometry and Number Theory · Alkaloids: synthesis and pharmacology
