On Hodge-Tate Decomposition Theorem

Since Scholze invented perfectoid spaces, many theorems of $p$-adic Hodge have been re-proven using the new tool. In this talk I will talk about the proof of Hodge-Tate Decomposition, which is $p$-adic version of classical Hodge decomposition. First I recall Fontaine’s beautiful idea in the case of abelian varieties. Next I focus on Scholze’s proof for general setting (rigid-analytic space) using perfectoid. If time permits then I will say something about integral parts.