Higher-dimensional 3-adic CM construction

DOI10.1016/j.jalgebra.2007.11.016zbMath1140.14042arXivmath/0607583OpenAlexW2166731133MaRDI QIDQ2475072

Robert Carls, David Lubicz, David R. Kohel

Publication date: 10 March 2008

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0607583

zbMATH Keywords

theta functionsmodular equationscanonical liftCM-methods

Mathematics Subject Classification ID

Theta functions and abelian varieties (14K25) Theta functions and curves; Schottky problem (14H42)

Related Items

Computing isogenies between abelian varieties ⋮ Examples of CM curves of genus two defined over the reflex field ⋮ Isogeny graphs of ordinary abelian varieties ⋮ GALOIS THEORY OF THE CANONICAL THETA STRUCTURE ⋮ Computing the 2-adic canonical lift of genus 2 curves ⋮ Computing Igusa class polynomials

Cites Work

• A quasi quadratic time algorithm for hyperelliptic curve point counting
• Multi-dimensional theta constant identities
• Fast computation of canonical lifts of elliptic curves and its application to point counting.
• Endomorphism rings of abelian surfaces and projective models of their moduli spaces
• On the equations defining Abelian varieties. I-III
• Examples of genus two CM curves defined over the rationals
• Handbook of Elliptic and Hyperelliptic Curve Cryptography
• Floating-Point LLL Revisited
• The 2-Adic CM Method for Genus 2 Curves with Application to Cryptography
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura
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