On tilts of certain infinite level shimura varieties
File(s)
Author(s)
Singer, Raffael
Type
Thesis
Abstract
Scholze's Siegel modular varieties $\cX_{\Gamma(p^\infty)}$ over a mixed characteristic perfectoid field are known to be perfectoid, yet their tilt remains somewhat elusive. We give two different methods to describe the tilt of spaces related to $\cX_{\Gamma(p^\infty)}$. The first, following an idea of Lurie, uses Drinfeld level structures to construct integral perfectoid models of infinite level Shimura curves. For the second method we show how to recover the Tate module of the universal family of abelian varieties from its anticanonical part together with the Weil pairing. This allows us to extend Scholze's description of the tilt of $\cX_{\Gamma_0(p^\infty)}(\epsilon)_a$ to level $\Gamma(p^\infty)$.
Version
Open Access
Date Issued
2020-09
Date Awarded
2021-02
Copyright Statement
Creative Commons Attribution NonCommercial Licence
License URL
Advisor
Buzzard, Kevin
Sponsor
Engineering and Physical Sciences Research Council
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)