The Convergent Topos in Characteristic p

  • Arthur Ogus
Part of the Modern Birkhäuser Classics book series (volume 88)


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.


Finite Type Canonical Isomorphism Coherent Sheaf Zariski Topology Zariski Open Subset 
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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

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

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