Analytic cyclic homology in positive characteristic

Abstract

Let $V$ be a complete discrete valuation ring with residue field $\mathbb{F}$. We define a cyclic homology theory for algebras over $\mathbb{F}$, 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 $\mathbb{F}$-algebra. We show that our theory is polynomially homotopy invariant, excisive, and matricially stable.

final version, to appear in Annals of K-theory

References in corpus (4)

• Dagger Geometry As Banach Algebraic Geometry
• Dagger completions and bornological torsion-freeness
• Nonarchimedean bornologies, cyclic homology and rigid cohomology
• Non-Archimedean analytic cyclic homology