Nonarchimedean bornologies, cyclic homology and rigid cohomology

GUILLERMO CORTIÑAS; GEORG TAMME; JOACHIM CUNTZ; RALF MEYER

DOCUMENTA MATHEMATICA

UNIV BIELEFELD

Año: 2018 vol. 23 p. 1197 - 1245

Let V be a complete discrete valuation ring with residue field kand with fraction field K of characteristic 0. We clarify the analysis be-hind the Monsky-Washnitzer completion of a commutative V -algebra usingspectral radius estimates for bounded subsets in complete bornologicalV -algebras. This leads us to a functorial chain complex for commutativek -algebras that computes Berthelot´s rigid cohomology. This chain complexis related to the periodic cyclic homology of certain complete bornologicalV -algebras