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Analytic cyclic homology in positive characteristic

Ralf Meyer and Devarshi Mukherjee
Vol. 8 (2023), No. 3, 379–419
DOI: 10.2140/akt.2023.8.379
Abstract

Let V be a complete discrete valuation ring with residue field 𝔽. We define a cyclic homology theory for algebras over 𝔽, by lifting them to free algebras over V , which we enlarge to tube algebras and complete suitably. We show that this theory may be computed using any pro-dagger algebra lifting of an 𝔽-algebra. We show that our theory is polynomially homotopy invariant, excisive, and matricially stable.

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Keywords
K-theory, cyclic homology, nonarchimedean functional analysis, bornologies
Mathematical Subject Classification
Primary: 19D55
Milestones
Received: 14 July 2022
Revised: 3 May 2023
Accepted: 23 May 2023
Published: 27 August 2023
Authors
Ralf Meyer
Mathematisches Institut
Universität Göttingen
Göttingen
Germany
Devarshi Mukherjee
Departmento de Matemática-IMAS
Universidad de Buenos Aires
Buenos Aires
Argentina
© 2023 The Author(s), under exclusive license to MSP (Mathematical Sciences Publishers).