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Rigid cohomology and \(p\)-adic point counting. (English) Zbl 1087.14020

In this expository article the author considers the problem of computing the zeta function of an algebraic variety defined over a finite field. He discusses \(p\)-adic algorithms relying upon rigid cohomology in some incarnation. The emphasis is on curves.

MSC:

14G10 Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture)
11G25 Varieties over finite and local fields
14G15 Finite ground fields in algebraic geometry
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