On the K-theory of Z/pn

Antieau B; Krause A; Nikolaus T

Abstract

We give an explicit algebraic description, based on prismatic cohomology, of the algebraic K-groups of rings of the form OK/I where K is a p-adic field and I is a non-trivial ideal in the ring of integers OK; this class includes the rings Z/pn where p is a prime. The algebraic description allows us to describe a practical algorithm to compute individual K-groups as well as to obtain several theoretical results: the vanishing of the even K-groups in high degrees, the determination of the orders of the odd K-groups in high degrees, and the degree of nilpotence of v1 acting on the mod p syntomic cohomology of Z/pn.