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The Overconvergent Site
Bernard Le Stum, Université de Rennes 1, France
A publication of the Société Mathématique de France.
Mémoires de la Société Mathématique de France
2011; 108 pp; softcover
Number: 127
ISBN-10: 2-85629-341-7
ISBN-13: 978-2-85629-341-6
List Price: US$37
Member Price: US$29.60
Order Code: SMFMEM/127
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The author proves that rigid cohomology can be computed as the cohomology of a site analogous to the crystalline site. Berthelot designed rigid cohomology as a common generalization of crystalline and Monsky-Washnitzer cohomology. Unfortunately, unlike the former, the functoriality of the theory is not built in. The author defines the "overconvergent site" which is functorially attached to an algebraic variety.

The author proves that the category of modules of finite presentation on this ringed site is equivalent to the category of overconvergent isocrystals on the variety. He also proves that their cohomology coincides.

A publication of the Société Mathématique de France, Marseilles (SMF), distributed by the AMS in the U.S., Canada, and Mexico. Orders from other countries should be sent to the SMF. Members of the SMF receive a 30% discount from list.


Graduate students and research mathematicians.

Table of Contents

  • Introduction
  • Geometry
  • Coefficients
  • Cohomology
  • Appendix
  • Bibliography
  • Index
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