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  3. Rigid Cohomology
  • Cited by 43
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    • Publisher:
      Cambridge University Press
      Publication date:
      09 October 2009
      06 September 2007
      ISBN:
      9780511543128
      9780521875240
      DOI:
      https://doi.org/10.1017/CBO9780511543128
      Dimensions:
      (228 x 152 mm)
      Weight & Pages:
      0.61kg, 336 Pages
      Dimensions:
      Weight & Pages:
      • Subjects:
      Mathematics (general), Mathematics, Number Theory, Geometry and Topology
      Series:
      Cambridge Tracts in Mathematics (172)
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    • Selected: Digital
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    Subjects:
    Mathematics (general), Mathematics, Number Theory, Geometry and Topology
    Series:
    Cambridge Tracts in Mathematics (172)
    Information

    Book description

    Dating back to work of Berthelot, rigid cohomology appeared as a common generalization of Monsky-Washnitzer cohomology and crystalline cohomology. It is a p-adic Weil cohomology suitable for computing Zeta and L-functions for algebraic varieties on finite fields. Moreover, it is effective, in the sense that it gives algorithms to compute the number of rational points of such varieties. This is the first book to give a complete treatment of the theory, from full discussion of all the basics to descriptions of the very latest developments. Results and proofs are included that are not available elsewhere, local computations are explained, and many worked examples are given. This accessible tract will be of interest to researchers working in arithmetic geometry, p-adic cohomology theory, and related cryptographic areas.

    Reviews

    '…written in a student friendly style.'

    Source: Zentralblatt MATH

    '… well-written, with a mixture of concrete examples and abstract theory. It is accessible to readers familiar with basic concepts of abstract algebraic geometry and p-adic analytic geometry.'

    Source: European Mathematical Society Newsletter

    '… a very nice book, poised to play a role of considerable importance in the literature. Its style is a bit terse but this should be no problem for the reader coming to this field, whose very interest in this fascinating subject bespeaks a commensurate maturity. This brand new book obviously fills an important niche.'

    Source: MAA Reviews

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