On tilts of certain infinite level shimura varieties

Raffael Singer
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...
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