Counting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology

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dc.creatorKedlaya, Kiran S.
dc.date2001-05-03
dc.date2001-11-20
dc.date.accessioned2026-07-07T06:31:12Z
dc.date.available2026-07-07T06:31:12Z
dc.descriptionWe 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+ε} n^{3+ε}).
dc.description10 pages; v2: corrected runtime exponent, added explanation of Lefschetz trace formula, corrected typos
dc.identifierhttps://arxiv.org/abs/math/0105031
dc.identifierhttp://arxiv.org/abs/math/0105031
dc.identifierpreprint; published version: J. Ramanujan Math. Soc. 16 (2001), 323-338; errata, ibid. 18 (2003), 417--418.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/98540
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject11G20, 11-04
dc.titleCounting Points on Hyperelliptic Curves using Monsky-Washnitzer Cohomology
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