An extension of Kedlaya's algorithm for hyperelliptic curves

DOI10.1016/j.jsc.2011.08.019zbMath1234.14001arXiv1006.4206OpenAlexW2049709309MaRDI QIDQ654037

Michael C. Harrison

Publication date: 21 December 2011

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1006.4206

zbMATH Keywords

Monsky-Washnitzer cohomologyKedlaya's algorithm

Mathematics Subject Classification ID

Elliptic curves (14H52) Software, source code, etc. for problems pertaining to algebraic geometry (14-04) Software, source code, etc. for problems pertaining to associative rings and algebras (16-04)

Related Items (10)

Explicit Vologodsky integration for hyperelliptic curves ⋮ Counting points on genus-3 hyperelliptic curves with explicit real multiplication ⋮ Computing zeta functions of cyclic covers in large characteristic ⋮ Explicit Coleman integration in larger characteristic ⋮ Zeta functions of nondegenerate hypersurfaces in toric varieties via controlled reduction in \(p\)-adic cohomology ⋮ Computing -series of geometrically hyperelliptic curves of genus three ⋮ Counting points on hyperelliptic curves in average polynomial time ⋮ Coleman integration for even-degree models of hyperelliptic curves ⋮ Counting points on hyperelliptic curves of genus 2 with real models ⋮ Two Recent p-adic Approaches Towards the (Effective) Mordell Conjecture

Uses Software

• Magma

Cites Work

• Counting points on \(C_{ab}\) curves using Monsky-Washnitzer cohomology
• A quasi quadratic time algorithm for hyperelliptic curve point counting
• Point counting in families of hyperelliptic curves
• The Magma algebra system. I: The user language
• An extension of Kedlaya's algorithm to hyperelliptic curves in characteristic \(2\)
• Formal cohomology. I
• Formal cohomology. II: The cohomology sequence of a pair
• Formal cohomology. III: Fixed point theorems
• Computing zeta functions of nondegenerate curves
• A p-Adic Quasi-Quadratic Time Point Counting Algorithm
• Relative Rigid Cohomology and Deformation of Hypersurfaces
• Algorithmic Number Theory
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