Back to Commutative Algebra Seminar: Fall 2018
Commutative Algebra Seminar
Date: Friday, Oct 26, 2018
Time: 2:30PM - 3:20PM
Location: LCB 215
Cris Negron
M.I.T., Boston
Title |
Cohomology for finite tensor categories and some fundamental operations |
Abstract |
This talk concerns the finite generation conjecture for finite tensor categories. One is free to think only of representation categories of finite-dimensional Hopf algebras here. The conjecture proposes that for any finite tensor category C, the self-extension algebra of the unit is a finitely generated algebra, and for any object V in C the extensions from the unit to V provide a finitely generated module over this algebra. This conjecture was proved for finite groups (in finite characteristic) by Golod, and Evans and Venkov, in which case C is rep(G), and for finite group schemes by Friedlander and Suslin. I will discuss how this finite generation property for cohomology behaves under certain ``fundamental operations" for tensor categories. I will spend much of the time discussing what these fundamental operations actually are, their general significance, and the specific examples of quantum groups and algebras of functions on group schemes. (For functions on a group scheme, we essentially want to understand how cohomology behaves under Hopf deformation.) This is joint work with Eric Friedlander and Julia Plavnik. |
Commutative Algebra