Hodge--Tate crystals and Sen theory

Abstract: Let $K$ be a finite extension of $\mathbb Q_p$. Bhatt and Scholze have proved that the category of prismatic $F$-crystals on the absolute prismatic site of $\mathcal O_K$ is equivalent to the category of crystalline $\mathbb Z_p$-representations of the absolute Galois group of $K$. In this talk, we will instead consider the (rational) Hodge--Tate crystals on the absolute prismatic site of $\mathcal O_K$ or more generally of a smooth $p$-adic formal scheme. We will show how Hodge--Tate crystals are related to the Sen theory. If time permits, we will also discuss its application in the arithmetic $p$-adic Simpson correspondence. This is joint work with Yupeng Wang.

number theory

Audience: researchers in the topic

London number theory seminar

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