On the $p$-adic theory of local models
Algebraic Geometry
2026-02-03 v2 Number Theory
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 -adic kimberlites, show that these include the v-sheaf local models, determine their special fibers using hyperbolic localization for the \'etale cohomology of small v-stacks, and analyze the resulting specialization morphism using convolution.
Keywords
Cite
@article{arxiv.2201.01234,
title = {On the $p$-adic theory of local models},
author = {Johannes Anschütz and Ian Gleason and João Lourenço and Timo Richarz},
journal= {arXiv preprint arXiv:2201.01234},
year = {2026}
}
Comments
Introduction updated; minor corrections