Descent for the K-theory of polynomial rings (Q1057324)

Let A be a commutative ring. Recall that NK\({}_ n\)(A) denotes the cokernel of \(K_ n(A)\to K_ n(A[X])\). This paper uses the known structure of \(NK_ n(A)\) as a module over the ring W(A) of big Witt vectors to show that \(NK_ n\) is almost an étale sheaf whose higher cohomology vanishes on Spec(A). If B is an étale A-algebra, we also express \(NK_ n(B)\) as a modified tensor product of \(NK_ n(A)\) and W(B). Some assumptions on n or A are needed in the proofs.