Picard groups and the algebraic K-theory of cuspidal singularities.

Seminar/Forum

Picard groups and the algebraic K-theory of cuspidal singularities.

Hesselholt has a conjectural calculation of the algebraic K-theory of \(k[x,y]/(x^b-y^a)\). 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 p-complete \(C{p^n}\)-spectra. This lets us use homological data to recognize, up to p-completion, when a \(C{p^n}\)-spectrum looks like a virtual representation sphere.

Presenter

  • Dr Vigleik Angeltveit
    Dr Vigleik Angeltveit, ANU