University of Chicago
Department of Mathematics

For finitely generated groups G, there turns out to be a connection between the density of integers n for which there is a normal subgroup of G of index n and complex linear algebraic groups admitting a dense homomorphism from G.

I will be discussing joint work with Randy McCarthy of UIUC in which we calculate the algebraic K-theory of a square-zero extension of F_p by a finite F_p-vector space after completion at p. The case of a one-dimensional vector space, namely that of the dual numbers over F_p, was done by Hesselholt-Madsen. We use a variant of topological cyclic homology whose construction is motivated by Goodwillie calculus.