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2006/240 (PDF) (PS) Last updated: 2007-01-10
Computing Zeta Functions of Nondegenerate Curves
W. Castryck, J. Denef, F. Vercauteren
Foundations

In this paper we present a $p$-adic algorithm to compute the zeta function of a nondegenerate curve over a finite field using Monsky-Washnitzer cohomology. The paper vastly generalizes previous work since all known cases, e.g. hyperelliptic, superelliptic and $C_{ab}$ curves, can be transformed to fit the nondegenerate case. For curves with a fixed Newton polytope, the property of being nondegenerate is generic, so that the algorithm works for almost all curves with given Newton polytope....

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