2022/12/12 by Devarshi Mukherjee, Mukherjee, Devarshi · 1 citation
Mathematics · #Mathematical and Theoretical Analysis #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2212.06262
We introduce bivariant K-theory for nonarchimedean bornological algebras over a complete discrete valuation ring V. This is the universal target for dagger homotopy invariant, matricially stable and excisive functors, similar to bivariant K-theory for locally convex topological ℂ-algebras and algebraic bivariant K-theory. When the first variable is the ground algebra V, we get a version of Weibel's homotopy algebraic K-theory, which we call stabilised overconvergent analytic K-theory. The resulting analytic K-theory satisfies dagger homotopy invariance, stability by completed matrix algebras, and excision.