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.
General
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