Picard groups and the algebraic Ktheory of cuspidal singularities.
Seminar/Forum
Hesselholt has a conjectural calculation of the algebraic Ktheory of \(k[x,y]/(x^by^a)\). It has remained a conjecture until now because nobody has been able to prove that a certain \(S^1\)equivariant space that comes up in the calculation is built from representation spheres in a specified way. I will explain how to sidestep this issue by computing the Picard group of the category of pcomplete \(C{p^n}\)spectra. This lets us use homological data to recognize, up to pcompletion, when a \(C{p^n}\)spectrum looks like a virtual representation sphere.
Presenter

Dr Vigleik Angeltveit, ANU