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 analytic the resulting specialization morphism using convolution.
Authors
Johannes Anschütz
Mathematisches Institut der Universität Bonn, Bonn, Germany
Current address:
Université Paris-Saclay, Laboratoire de mathématiques d'Orsay, Orsay, France
Ian Gleason
Mathematisches Institut der Universität Bonn, Bonn, Germany
Current address:
Department of Mathematics, National University of Singapore, Singapore
João Lourenço
Max-Planck-Institut für Mathematik, 53111 Bonn, Germany
Current address:
Université Sorbonne Paris Nord (Paris 13), Villetaneuse, France
Timo Richarz
Department of Mathematics, Technische Universität Darmstadt, Darmstadt, Germany
