This is a small seminar we ran on Étale cohomology over the summer organized by Vidhu Adhihetty and myself. We had scheduling issues since most people were traveling so we couldn't finish.
Location: Room 622
Meeting Time: Thursdays 11:00am EST
Syllabus: Found here
1. Introduction
Vidhu Adhihetty 06/19/25
We introduce the Weil conjectures as motivation for Étale cohomology and go over étale morphisms. Notes available here.
2. Sites and Sheaves
Wenqi Li 6/26/25
We introduce the notion of a site and a Grothendieck topology. We then prove faithfully flat descent. Notes available here.
3. More on sheaves
Nicolás Vilches 7/3/25
We continue the discussion from last week, specializing to sheaves on the étale sites. Notes available here.
4. Sheaf Cohomology
Carlos Andrés Alvarado Álvarez 7/10/25
We prove that the category of sheaves is abelian and has enough injectives to define étale cohomology.
5. Cech Cohomology
Carlos Andrés Alvarado Álvarez 7/18/25
We define Cech covers and Cech cohomology and relate it to étale cohomology.
6. Torsors and H^1
Vidhu Adhihetty 7/23/25
We will explain étale G-torsors over X and explain how these torsors are in bijection with elements of H^1(X,G).