##### Department of Mathematics,

University of California San Diego

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### Math 209 - Number Theory Seminar

## Tong Liu

#### Purdue University

## Prismatic F-crystal and lattice in crystalline representation

##### Abstract:

In this talk, I will explain a theorem of Bhatt-Scholze: the equivalence between prismatic $F$-crystal and $\mathbb Z_p$-lattices inside crystalline representation, and how to extend this theorem to allow more general types of base ring like Tate algebra ${\mathbb Z}_p\langle t^{\pm 1}\rangle$. This is a joint work with Heng Du, Yong-Suk Moon and Koji Shimizu.

This is a talk in integral $p$-adic Hodge theory. So in the pre-talk, I will explain the motivations and base ideas in integral $p$-adic Hodge theory.

### January 13, 2022

### 2:00 PM

Pre-talk at 1:30 PM

APM 6402 and Zoom;

see https://www.math.ucsd.edu/~nts

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