Weak completions, bornologies and rigid cohomology

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.

14 pages. arXiv admin note: text overlap with arXiv:1708.00357

References in corpus (1)

• Nonarchimedean bornologies, cyclic homology and rigid cohomology