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Algebraic Topology Seminar

The singularity category of the cochains of classifying spaces of finite groups [joint work with G.Stevenson and D.Benson]

Monday, November 16, 2020
11:00 AM-12:00 PM
online Off Campus Location
For an ordinary commutative Noetherian ring R we would define the singularity category to be the quotient of the (derived category of) finitely generated modules modulo the (derived category of) fg projective modules [``the bounded derived category modulo compact objects’’]. This is trivial if and only if R is regular.

To cover cochains on the classifying space, with coefficients in a field k of characteristic p we take C^*(BG;k) to be the commutative ring spectrum of maps from BG to the Eilenberg-MacLane spectrum, and work in the category of module spectra over it. it is then easy to define the compact objects, but finitely generated objects need more ingenuity. The talk will describe the definition and show that the singularity category is trivial exactly when G is p-nilpotent. We will go on to describe the singularity category for groups with cyclic Sylow p-subgroup.
Speaker(s): John Greenlees (University of Warwick)
Building: Off Campus Location
Location: Virtual
Event Type: Workshop / Seminar
Tags: Mathematics
Source: Happening @ Michigan from Department of Mathematics