Verschiebung maps among K-groups of truncated polynomial algebras

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Horiuchi, Ryo¹ 

[1] Kure Coll, Natl Inst Technol KOSEN, Kure, Hiroshima, Japan

关键词: Algebraic K-theory;    Topological Hochschild homology;    Perfectoid field;   

DOI  :  10.1016/j.jpaa.2020.106641

来源: Elsevier

【 摘 要 】

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]/(x(m)), (x)) -> Kq+1 (A[x]/(x(mn)), (x)), induced by the ring homomorphism A[x]/(x(m)) -> A[x]/(x(mn)), x bar right arrow x(n). We evaluate these maps, up to extension, for general A in terms of topological Hochschild homology, and for regular F-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. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free