Verschiebung maps among K-groups of truncated polynomial algebras

2017/12/08 by Ryo Horiuchi, Horiuchi, Ryo
Mathematics · #Advanced Topics in Algebra #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.1712.03189

openalex publication_date 2017/12/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

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