Work

On the $p$-adic theory of local models

Year: 2026

Type: article

Abstract: We prove the Scholze--Weinstein conjecture on the existence and uniqueness of local models for local Shimura varieties, as well as the test function conjecture of Haines--Kottwitz in this framework. To this end, we establish a specialization principle for well-behaved $p$-adic kimberlites, show that these include the v-sheaf local models, determine their special fibers using hyperbolic localization for the étale cohomology of small v-stacks, and analyze the resulting specialization morphism using convolution.

Source: Annals of Mathematics

DOI: 10.4007/annals.2026.204.3.2

Authors: Johannes Anschütz, Ian Gleason, João Lourenço, Timo Richarz

Institutions: University of Bonn, Université Sorbonne Paris Nord, Technische Universität Darmstadt

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W4226513351

FWCI: 104.5

Cites: 8

Cited by: 66

Related to: 10