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Diophantine equations, rational points, abelian varieties, Arakelov theory, Iwasawa theory.

3 votes

What are the potential applications of perfectoid spaces to homotopy theory?

Edit Sep 2023: the ideas below have now been developed more thoroughly in my new paper Prisms and Tambara functors I As Peter points out, it is more reasonable to look for connections between prisms …
Yuri Sulyma's user avatar
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46 votes
2 answers
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What are the potential applications of perfectoid spaces to homotopy theory?

This year's Arizona Winter School was on perfectoid spaces, and there were quite a few homotopy theorists in the audience. I'd like to get a "big list" of reasons homotopy theorists might care about p …