Nonarchimedean bivariant K-theory

Devarshi Mukherjee

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arXiv · 2212.06262

Nonarchimedean bivariant K-theory

Devarshi Mukherjee

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Abstract

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 $\mathbb{C}$-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 \textit{stabilised overconvergent analytic K-theory}. The resulting analytic K-theory satisfies dagger homotopy invariance, stability by completed matrix algebras, and excision.

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Devarshi Mukherjee. 2022-12-12. Nonarchimedean bivariant K-theory. https://arxiv.org/abs/2212.06262

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