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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. © 2018 Elsevier B.V.

Registro:

Documento: Artículo
Título:Weak completions, bornologies and rigid cohomology
Autor:Cortiñas, G.; Cuntz, J.; Meyer, R.; Tamme, G.
Filiación:Dep. Matemática-IMAS, FCEyN-UBA, Ciudad Universitaria Pab 1, 1428 Buenos Aires, Argentina
Mathematisches Institut, Westfälische Wilhelms-Universität Münster, Einsteinstr. 62, Münster, 48149, Germany
Mathematisches Institut, Georg-August Universität Göttingen, Bunsenstraße 3–5, Göttingen, 37073, Germany
Universität Regensburg, Fakultät für Mathematik, Regensburg, 93040, Germany
Palabras clave:Algebraic geometry; Bornological algebras; Cyclic homology; Overconvergent completions; Positive characteristic; Rigid cohomology
Año:2018
Volumen:129
Página de inicio:192
Página de fin:199
DOI: http://dx.doi.org/10.1016/j.geomphys.2018.03.005
Título revista:Journal of Geometry and Physics
Título revista abreviado:J. Geom. Phys.
ISSN:03930440
CODEN:JGPHE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_03930440_v129_n_p192_Cortinas

Referencias:

  • Monsky, P., Washnitzer, G., Formal cohomology. I (1968) Ann. of Math. (2), 88, pp. 181-217
  • Elkik, R., Solutions d’équations à coefficients dans un anneau hensélien (1973) Ann. Sci. Éc. Norm. Supér. (4), 6, pp. 553-603. , (in French)
  • Berthelot, P., Cohomologie rigide et cohomologie rigide à supports propres. Première partie, preprint; Besser, A., Syntomic regulators and p-adic integration. I. Rigid syntomic regulators (2000) Proceedings of the Conference on P-Adic Aspects of the Theory of Automorphic Representations (Jerusalem, 1998), pp. 291-334
  • (2017), arXiv:1708.00357 Guillermo Cortiñas, Joachim Cuntz, Ralf Meyer, Georg Tamme, Nonarchimedean bornologies, cyclic homology and rigid cohomology; Große Klönne, E., De Rham cohomology of rigid spaces (2004) Math. Z., 247 (2), pp. 223-240
  • Fulton, W., A note on weakly complete algebras (1969) Bull. Amer. Math. Soc., 75, pp. 591-593
  • Berthelot, P., Finitude et pureté cohomologique en cohomologie rigide (1997) Invent. Math., 128 (2), pp. 329-377. , (in French). With an appendix in English by Aise Johan de Jong
  • Große-Klönne, E., Rigid analytic spaces with overconvergent structure sheaf (2000) J. Reine Angew. Math., 519, pp. 73-95

Citas:

---------- APA ----------
Cortiñas, G., Cuntz, J., Meyer, R. & Tamme, G. (2018) . Weak completions, bornologies and rigid cohomology. Journal of Geometry and Physics, 129, 192-199.
http://dx.doi.org/10.1016/j.geomphys.2018.03.005
---------- CHICAGO ----------
Cortiñas, G., Cuntz, J., Meyer, R., Tamme, G. "Weak completions, bornologies and rigid cohomology" . Journal of Geometry and Physics 129 (2018) : 192-199.
http://dx.doi.org/10.1016/j.geomphys.2018.03.005
---------- MLA ----------
Cortiñas, G., Cuntz, J., Meyer, R., Tamme, G. "Weak completions, bornologies and rigid cohomology" . Journal of Geometry and Physics, vol. 129, 2018, pp. 192-199.
http://dx.doi.org/10.1016/j.geomphys.2018.03.005
---------- VANCOUVER ----------
Cortiñas, G., Cuntz, J., Meyer, R., Tamme, G. Weak completions, bornologies and rigid cohomology. J. Geom. Phys. 2018;129:192-199.
http://dx.doi.org/10.1016/j.geomphys.2018.03.005