Algebra/Topology seminar

Akhil Mathew (UChicago), Rigidity in algebraic K-theory and topological cyclic homology

Abstract: We show that for a henselian pair (R, I), the relative K-theory
and relative topological cyclic homology with mod p coefficients agree.
This yields a generalization of the Gabber-Gillet-Suslin-Thomason rigidity
theorem (when p is invertible on the ring) and the Dundas-McCarthy theorem
(when I is nilpotent). This recovers several computations in p-adic
algebraic K-theory and leads to some new structural results. Our methods
are based on the new description of the homotopy theory of cyclotomic
spectra given by Nikolaus and Scholze. This is joint work with Dustin
Clausen and Matthew Morrow.