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arXiv · 1712.08004

Weak completions, bornologies 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 $k$ of positive characteristic and with fraction field $K$ of characteristic 0. We clarify the analysis behind the Monsky--Washnitzer completion of a commutative $V$-algebra using completions of bornological $V$-algebras. This leads us to a functorial chain complex for a finitely generated commutative algebra over the residue field $k$ that computes its rigid cohomology in the sense of Berthelot.

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Guillermo Cortiñas, Joachim Cuntz, Ralf Meyer, Georg Tamme. 2017-12-20. Weak completions, bornologies and rigid cohomology. https://doi.org/10.1016/j.geomphys.2018.03.005

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