Back to Algebraic Geometry Seminar: Spring 2024
Algebraic Geometry Seminar
Date: Tuesday, Feb 20, 2024
Time: 3:30PM - 4:30PM
Location: LCB 222
Gabriel Dorfsman-Hopkins
St. Lawrence University
Title |
A Condensed Approach to Continuous Group Cohomology |
Abstract |
A common issue one can run into is that topological algebra doesn’t play well with homological algebra: for example, the category of topological abelian groups is not an abelian category. This introduces many pathologies, for example: continuous group cohomology does not give rise to long exact sequences. Clausen and Scholze (resp, Barwick and Haine) suggest a solution to this kind of problem by extending the category of topological abelian groups to the abelian category of condensed abelian groups (resp. pyknotic abelian groups), which are sheaves of abelian groups on the pro-etale site of a geometric point. We will explain a construction of continuous group cohomology in this condensed setting, give comparisons to classical continuous group cohomology, and explain some consequences and future directions that fall out of this formalism (including, if time allows, to p-adic and perfectoid geometry). |
Algebraic Geometry