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arXiv · 1708.00357

Nonarchimedean bornologies, cyclic homology and rigid cohomology

Guillermo Cortiñas·Joachim Cuntz·Ralf Meyer·Georg Tamme
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Abstract

Let $V$ be a complete discrete valuation ring with residue field $k$ and with fraction field $K$ of characteristic 0. We clarify the analysis behind the Monsky--Washnitzer completion of a commutative $V$-algebra using spectral radius estimates for bounded subsets in complete bornological $V$-algebras. This leads us to a functorial chain complex for commutative $k$-algebras that computes Berthelot's rigid cohomology. This chain complex is related to the periodic cyclic homology of certain complete bornological $V$-algebras.

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Guillermo Cortiñas, Joachim Cuntz, Ralf Meyer, Georg Tamme. 2017-08-01. Nonarchimedean bornologies, cyclic homology and rigid cohomology. https://doi.org/10.25537/dm.2018v23.1197-1245

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