On the Ubiquity of “Pathology” in Products

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


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
$$H_{cris}^ * (X/{W_n}(k)) \simeq {H^ * }(X,{W_n}\Omega _X^ * )$$


Tensor Product Convex Polygon Inverse Limit Canonical Isomorphism Newton Polygon 
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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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