## Arithmetic Geometry and Number Theory RTG Seminar: The comparison theorem for algebraic stacks

Seminar | December 11 | 3:10-5 p.m. | 891 Evans Hall

Chang-Yeon Chough, Institute for Basic Science

Department of Mathematics

Michael Artin and Barry Mazur's classical comparison theorem tells us that for a pointed connected finite type $\mathbb C$-scheme $X$, there is a map from the singular complex associated to the underlying topological spaces of the analytification of $X$ to the étale homotopy type of $X$, and it induces an isomorphism on profinite completions. I'll begin with a brief review on Artin-Mazur's étale homotopy theory of schemes, and explain how I extended it to algebraic stacks under model category theory. Finally, I'll provide a formal proof of the comparison theorem for algebraic stacks using a new characterization of profinite completions.

yxy@berkeley.edu