Tubular neighborhoods of local models

Ian Gleason; João Lourenço

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arXiv · 2204.05526

Tubular neighborhoods of local models

Ian Gleason·João Lourenço

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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 Ansch\"{u}tz and Richarz are always normal with reduced special fiber, thereby establishing the remaining cases of the geometric part of the Scholze$-$Weinstein conjecture when $p \leq 3$. 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.

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BibTeX RIS

Ian Gleason, João Lourenço. 2022-04-12. Tubular neighborhoods of local models. https://arxiv.org/abs/2204.05526

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