##### Department of Mathematics,

University of California San Diego

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### Math 292: Topology Seminar

## Peter Haine

#### University of California, Berkeley

## New perspectives on the étale homotopy type

##### Abstract:

Étale homotopy theory was invented by Artin and Mazur in the 1960s as a way to associate to a scheme X, a homotopy type with fundamental group the étale fundamental group of X and whose cohomology captures the étale cohomology of X with locally constant constructible coefficients. In this talk we'll explain how to construct a stratified refinement of the étale homotopy type that classifies constructible étale sheaves and gives rise to a new definition of the étale homotopy type. The stratified étale homotopy type also plays a role in the reconstruction of schemes: in nice cases, schemes can be completely reconstructed from their stratified étale homotopy types. This is joint work with Clark Barwick and Saul Glasman.

Host: Zhouli Xu

### October 18, 2022

### 4:30 PM

APM 7218

Research Areas

Geometry and Topology****************************