Local cyclic homology for nonarchimedean Banach algebras

2022/04/01 by Devarshi Mukherjee, Ralf Meyer, Mukherjee, Devarshi +1
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2204.00508

openalex publication_date 2022/04/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let V be a complete discrete valuation ring with uniformiser p. We introduce an invariant of Banach V-algebras called local cyclic homology. This invariant is related to analytic cyclic homology for complete, bornologically torsionfree V-algebras. It is shown that local cyclic homology only depends on the reduction mod p of a Banach V-algebra and that it is homotopy invariant, matricially stable, and excisive.

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