Hecke actions on the K-theory of commutative rings

Abstract

We prove that in the case of a Galois extension of commutative rings R ⊂- S with Galois group G, the correspondence H → K i ( S H ) ( H ≤ G) defines a cohomological G-functor. This gives a partial generalisation of results of Roggenkamp, Scott and Verschoren who consider the case of Picard groups. We use the equivalence of cohomological G-functors and Hecke actions (Yoshida, 1983) to derive some results about the structure of K-theory groups of rings of algebraic integers.