Full Level Structures on Elliptic Curves

Full Level Structures on Elliptic Curves

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Jacob Lurie, IAS
Fine Hall 322

Let p be a prime number, and let M denote the moduli stack of elliptic curves equipped with an infinite level structure at the prime p.

Scholze has shown that the generic fiber of M is a perfectoid space. In this talk, I'll discuss an integral refinement of this result, as well as some ``approximate'' results which hold at finite level.