Algebraic Topology Seminar

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 of spaces. We'll also explain how this refinement gives rise to a new, concrete definition of the étale homotopy type. This is joint work with Clark Barwick and Saul Glasman. Speaker(s): Peter Haine (MIT)