Bonn Topology Group - Abstracts

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Talk

June 12th 2018
Beren Sanders (EPF Lausanne, Switzerland): Quillen stratification for the Balmer spectrum with applications

Abstract

I will begin with some historical background on the spectrum of the cohomology ring and its significance in modular representation theory. Then, after discussing thick subcategory classification theorems and the spectrum of a tensor triangulated category, I will explain how one can obtain a new proof of the Benson-Carlson-Rickard theorem by lifting Quillen stratification to the categorical level. While a new proof of a 20 year old theorem might not sound too exciting, the same approach gives a promising strategy for proving analogous classification theorems in other as yet poorly understood examples. In particular, I will discuss a work-in-progress application of these ideas to the problem of classifying the thick tensor-ideals of the stable category of the mod p Steenrod algebra (at least when p=2).

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