TUBULAR NEIGHBORHOODS OF LOCAL MODELS

We show that the v-sheaf local models of Scholze and Weinstein are unibranch. In particular, this proves that the scheme-theoretic local models defined in Ansch & uuml;tz, Gleason, Louren & ccedil;o, 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 <= 3. Our methods are general, topological, and simplify those of Zhu for tamely ramified groups in positive characteristic. As a technical input, we generalize a comparison theorem of nearby cycles of Huber to the v-sheaf setup.