The Grothendieck Festschrift pp 133-162

Part of the Progress in Mathematics book series (MBC, volume 88)

The Convergent Topos in Characteristic p

  • Arthur Ogus


The purpose of this note is to investigate some of the foundational questions concerning convergent cohomology as introduced in [?] and [?], using the language and techniques of Grothendieck topologies. In particular, if X is a scheme of finite type over a perfect field k of characteristic p and with Witt ring W, we define the “convergent topos (X/W)conv, and we study the cohomology of its structure sheaf OX/W and of KX := QOX/W. Since the topos (X/W)conv is not noetherian, formation of cohomology does not commute with tensor products, and these are potentially quite different.


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Copyright information

© Springer Science+Business Media New York 1990

Authors and Affiliations

  • Arthur Ogus
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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