##### Department of Mathematics,

University of California San Diego

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### RTG Colloquium in Algebra/Algebraic Geometry/Number Theory

## Tong Liu

#### Purdue University and UCSD

## p-torsion etale cohomology and de Rham cohohomology. How to read arithmetic from geometry.

##### Abstract:

Classical comparison theorem established the isomorphism between singular cohomology and de Rham cohomology for smooth manifolds. The p-adic analogy aims to compare p-adic etale cohomology to de Rham cohomology for projective smooth schemes. In this talk, I will review and explain p-torsion version of such comparison and discuss how prismatic cohomology, recently invented by Bhatt-Scholze, can help to promote such p-torsion comparison. This is joint work with Shizhang Li.

Organizer: UCSD RTG Group in Algebra/Alg.Geometry/Number Theory

### June 8, 2022

### 5:00 PM

Zoom meeting ID: 96603729735

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