Algebra seminar - Jason Semararo - The ideal spectrum of the Chern subring of a fusion system
| Dates: | 14 November 2023 |
|---|
| Times: | 14:00 - 15:00 |
|---|
| What is it: | Seminar |
|---|
| Organiser: | Department of Mathematics |
|---|
| Who is it for: | University staff, External researchers, Current University students |
|---|
| Speaker: | Jason Semararo |
|---|
|
I will report on some joint work with Ian Leary. It is a classical fact that the even degree elements in the cohomology of a finite group G over a field of characteristic p form a finitely generated commutative ring. Quillen showed that the ideal spectrum of this ring is stratified by pieces coming from the elementary abelian p-subgroups of G. A fusion system on a finite p-group S is a category on the subgroups of S with injective morphisms satisfying some weak "Sylow" axioms motivated by properties of G-conjugation when S is Sylow in G. As for a group G, the cohomology of a fusion system is the subring of stable elements in the cohomology of S. We define the Chern subring of this ring, consisting of Chern classes of fusion stable S-representations, and prove that this too enjoys a Quillen stratification, simultaneously generalising results of Linckelmann and Green--Leary. If time permits, I will discuss a related (mathematical) hope and dream that vector bundles might provide topological alternatives to representations in this story.
Speaker
Jason Semararo
Organisation: University of Loughborough
Travel and Contact Information
Find event
Frank Adams 1
Alan Turing Building
Manchester
