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. For a genus g curve over F_{p^n}, the
expected running time is O(n^3g^6 + n^2g^{6.5}), whereas the space complexity
amounts to O(n^3g^4), assuming p is fixed.Comment: 41 page
