Semistable models for modular curves of arbitrary level

• 成果类型: Article
• 署名作者: Weinstein, Jared
• 署名单位: Boston University
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-015-0641-5
• 发表日期: 2016
• 页码: 459-526
• 关键词: deformation spaces; stable reduction

摘要

We produce an integral model for the modular curve over the ring of integers of a sufficiently ramified extension of whose special fiber is a semistable curve in the sense that its only singularities are normal crossings. This is done by constructing a semistable covering (in the sense of Coleman) of the supersingular part of , which is a union of copies of a Lubin-Tate curve. In doing so we tie together non-abelian Lubin-Tate theory to the representation-theoretic point of view afforded by Bushnell-Kutzko types. For our analysis it was essential to work with the Lubin-Tate curve not at level but rather at infinite level. We show that the infinite-level Lubin-Tate space (in arbitrary dimension, over an arbitrary nonarchimedean local field) has the structure of a perfectoid space, which is in many ways simpler than the Lubin-Tate spaces of finite level.