Nonarchimedean bivariant -theory

  • Devarshi Mukherjee

    Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina
Nonarchimedean bivariant $K$-theory cover

A subscription is required to access this article.

Abstract

We introduce bivariant -theory for nonarchimedean bornological algebras over a complete discrete valuation ring . This is the universal target for dagger homotopy invariant, matrically stable, and excisive functors, similar to bivariant -theory for locally convex topological -algebras and algebraic bivariant -theory. As in the archimedean case, we use the universal property to construct a bivariant Chern character into analytic and periodic cyclic homology. When the first variable is the ground algebra , we get a version of Weibel’s homotopy algebraic -theory, which we call stabilised overconvergent analytic -theory. The resulting analytic -theory satisfies dagger homotopy invariance, stability by completed matrix algebras, and excision.

Cite this article

Devarshi Mukherjee, Nonarchimedean bivariant -theory. J. Noncommut. Geom. (2024), published online first

DOI 10.4171/JNCG/562