Rigorous computation of the endomorphism ring of a Jacobian

Abstract

We describe several improvements to algorithms for the rigorous computation of the endomorphism ring of the Jacobian of a curve defined over a number field.

37 pages, 1 figure; v5 missing reference added

References in corpus (5)

• Rigorous computation of the endomorphism ring of a Jacobian
• A database of genus 2 curves over the rational numbers
• Computing the geometric endomorphism ring of a genus 2 Jacobian
• Real multiplication through explicit correspondences
• Lifts of Hilbert modular forms and application to modularity of abelian varieties

Cited by in corpus (24)

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• A database of nonhyperelliptic genus 3 curves over Q
• A numerical transcendental method in algebraic geometry
• Explicit Kummer Theory for Elliptic Curves
• Numerical computation of endomorphism rings
• Effective obstruction to lifting Tate classes from positive characteristic
• Lifts of Hilbert modular forms and application to modularity of abelian varieties
• Vanishing criteria for Ceresa cycles
• Some extensions of the modular method and Fermat equations of signature $(13,13,n)$
• Examples of genuine QM abelian surfaces which are modular
• Geometric quadratic Chabauty and $p$-adic heights
• Computing isogenies from modular equations in genus two
• A semi-numerical algorithm for the homology lattice and periods of complex elliptic surfaces over the projective line
• Effective homology and periods of complex projective hypersurfaces
• Separation of periods of quartic surfaces
• Moduli for rational genus 2 curves with real multiplication for discriminant 5
• Automorphisms of Abelian Varieties and Principal Polarizations
• Evaluating modular equations for abelian surfaces
• Endomorphism algebras of abelian varieties with large cyclic 2-torsion field over a given field