On the Ubiquity of “Pathology” in Products

  • Nicholas M. Katz
Part of the Progress in Mathematics book series (PM, volume 35)

Abstract

Fix a prime number p, and an algebraically closed field k of characteristic p. For any proper smooth k-scheme X, we denote by
$$W\Omega _X^. = \mathop {\lim }\limits_{\overleftarrow n } {W_n}\Omega _X^.$$
its DeRham-Witt complex. One knows (c.f. [Ill, 1, 2]) that WΩ X calculates the crystalline cohomology of X, i.e., one has a canonical isomorphism
$$H_{cris}^*(X) \simeq {H^ * }(X,W\Omega _X^ \bullet )$$
, which is the inverse limit of canonical isomorphisms
$$H_{cris}^ * (X/{W_n}(k)) \simeq {H^ * }(X,{W_n}\Omega _X^ * )$$
.

Keywords

Tensor Product Convex Polygon Inverse Limit Canonical Isomorphism Newton Polygon 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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Copyright information

© Springer Science+Business Media New York 1983

Authors and Affiliations

  • Nicholas M. Katz
    • 1
  1. 1.Department of MathematicsPrinceton UnivesityPrincetonUSA

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