K-theory of cuspidal curves over a perfectoid base and formal analogues

Abstract

In this paper we continue the work of using the recent advances in algebraic K-theory to extend computations done in characteristic p to the mixed characteristic setting using perfectoid rings. We extend the work of Hesselholt-Nikolaus in [18] on the algebraic K-Theory of cuspidal curves. We consider both cuspidal curves and the p-completion of cuspidal curves. Along the way we also study the K-theory of the p-completed affine line over a perfectoid ring.