Geodesic
Nonarchimedean Bornologies, Cyclic Homology and Rigid Cohomology
Documenta mathematica, Tome 23 (2018), pp. 1197-1245.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14F30, 14F40, 19D55, 14G22, 13D03
Keywords: bornological algebra, rigid cohomology, periodic cyclic homology 
@article{DOCMA_2018__23__a27,
     author = {Corti\~nas, Guillermo and Cuntz, Joachim and Meyer, Ralf and Tamme, Georg},
     title = {Nonarchimedean {Bornologies,} {Cyclic} {Homology} and {Rigid} {Cohomology}},
     journal = {Documenta mathematica},
     pages = {1197--1245},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a27/}
}
TY  - JOUR
AU  - Cortiñas, Guillermo
AU  - Cuntz, Joachim
AU  - Meyer, Ralf
AU  - Tamme, Georg
TI  - Nonarchimedean Bornologies, Cyclic Homology and Rigid Cohomology
JO  - Documenta mathematica
PY  - 2018
SP  - 1197
EP  - 1245
VL  - 23
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a27/
LA  - en
ID  - DOCMA_2018__23__a27
ER  - 
%0 Journal Article
%A Cortiñas, Guillermo
%A Cuntz, Joachim
%A Meyer, Ralf
%A Tamme, Georg
%T Nonarchimedean Bornologies, Cyclic Homology and Rigid Cohomology
%J Documenta mathematica
%D 2018
%P 1197-1245
%V 23
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a27/
%G en
%F DOCMA_2018__23__a27
Cortiñas, Guillermo; Cuntz, Joachim; Meyer, Ralf; Tamme, Georg. Nonarchimedean Bornologies, Cyclic Homology and Rigid Cohomology. Documenta mathematica, Tome 23 (2018), pp. 1197-1245. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a27/