论文标题
无限级别的模块化曲线的尖口和$ Q $ - 膨胀原理
Cusps and $q$-expansion principles for modular curves at infinite level
论文作者
论文摘要
我们开发了Scholze的$ P $ ADIC模块化曲线的尖牙的分析理论，该曲线在泰特曲线的完美素参数空间方面。作为一种应用，我们描述了模块化曲线普通基因座的反倾向过度邻域（$γ_1（p^\ infty）$）与无限水平完善Igusa品种的类似基因座之间的典型倾斜同构。我们还证明，在无限级别的模块化曲线上功能的各种$ q $膨胀原则，即，延伸到牙孔的属性，消失，来自有限的水平并受到界限，都可以在$ q $ - expansions上检测到。
We develop an analytic theory of cusps for Scholze's $p$-adic modular curves at infinite level in terms of perfectoid parameter spaces for Tate curves. As an application, we describe a canonical tilting isomorphism between an anticanonical overconvergent neighbourhood of the ordinary locus of the modular curve at level $Γ_1(p^\infty)$ and the analogous locus of an infinite level perfected Igusa variety. We also prove various $q$-expansion principles for functions on modular curves at infinite level, namely that the properties of extending to the cusps, vanishing, coming from finite level, and being bounded, can all be detected on $q$-expansions.
