Verschiebung maps among K-groups of truncated polynomial algebras

الأصل · EN

Let p be a prime number, and let A be a ring in which p is nilpotent. In this paper, we consider the maps Kq₊₁(A[x]/(xᵐ), (x))→ Kq₊₁(A[x]/(xmn), (x)),induced by the ring homomorphism A[x]/(xᵐ)→ A[x]/(xmn), x xⁿ. We evaluate these maps, up to extension, for general A in terms of topological Hochschild homology, and for regular Fₚ-algebras A, in terms of groups of de Rham-Witt forms. After the evaluation, we give a calculation of the relative K-group of Oₖ/pOₖ for certain perfectoid fields K.