Tubular neighborhoods of local models

Abstract

We show that the v-sheaf local models of moduli spaces of $p$-adic shtukas are unibranch. In particular, this proves that the scheme-theoretic local models defined in our joint work with Anschütz and Richarz are always normal with reduced special fiber, thereby establishing the remaining cases of the geometric part of the Scholze$-$Weinstein conjecture when $p\le 3$. Our methods are general, topological, and simplify Zhu's proof of the coherence conjecture. As a technical input, we generalize a comparison theorem of nearby cycles of Huber to the v-sheaf setup.

arXiv commentFinal version submitted to journal before the journal's editorial reviews