Monday, January 24, 2022
4:00 PM - 5:00 PM
Linde Hall 387
Algebra and Geometry Seminar
Stratified étale homotopy theory
Peter Haine, Department of Mathematics, UC Berkeley,
Étale homotopy theory was invented by Artin and Mazur in the 1960s as a way to associate to a scheme S, a homotopy type with fundamental group the étale fundamental group of S and whose cohomology captures the étale cohomology of S 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 of spaces. We'll also explain how this refinement gives rise to a new, concrete definition of the étale homotopy type. We'll then explain how to use condensed math to upgrade this result from discrete rings to rings with a topology such as Z_\ell, Q_\ell, or F_q[[t]]. This is joint work with Clark Barwick and Saul Glasman.
For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected].