Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology

Details Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology

2001-05-03

arxiv.org/abs/math/0105031v2

preprint; published version: J. Ramanujan Math. Soc. 16 (2001), 323-338; errata, ibid. 18 (2003), 417--418.

Mathematics

Algebraic Geometry

10 pages; v2: corrected runtime exponent, added explanation of Lefschetz trace formula, corrected typos

Scientific paper

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}).

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