Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology
Algebraic Geometry
2007-05-23 v2 Number Theory
Abstract
We describe an algorithm for counting points on an arbitrary hyperelliptic curve over a finite field of odd characteristic, using Monsky-Washnitzer cohomology to compute a p-adic approximation to the characteristic polynomial of Frobenius. For fixed p, the asymptotic running time for a curve of genus g over the field of p^n elements is O(g^{4+\epsilon} n^{3+\epsilon}).
Keywords
Cite
@article{arxiv.math/0105031,
title = {Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology},
author = {Kiran S. Kedlaya},
journal= {arXiv preprint arXiv:math/0105031},
year = {2007}
}
Comments
10 pages; v2: corrected runtime exponent, added explanation of Lefschetz trace formula, corrected typos