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arXiv · 1912.09366

Non-Archimedean analytic cyclic homology

Guillermo Cortiñas·Ralf Meyer·Devarshi Mukherjee
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Abstract

Let $V$ be a complete discrete valuation ring with fraction field $F$ of characteristic zero and with residue field $\mathbb{F}$. We introduce analytic cyclic homology of complete torsion-free bornological algebras over $V$. We prove that it is homotopy invariant, stable, invariant under certain nilpotent extensions, and satisfies excision. We use these properties to compute it for tensor products with dagger completions of Leavitt path algebras. If $R$ is a smooth commutative $V$-algebra of relative dimension $1$, then we identify its analytic cyclic homology with Berthelot's rigid cohomology of $R\otimes_{V}\mathbb{F}$.

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Guillermo Cortiñas, Ralf Meyer, Devarshi Mukherjee. 2019-12-19. Non-Archimedean analytic cyclic homology. https://doi.org/10.25537/dm.2020v25.1353-1419

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