On the modular curve X0 (23) Ren´e Schoof Abstract. The Jacobian J0 (23) of the modular curve X0 (23) is a semi-stable abelian variety over Q with good reduction outside 23. It is simple. We prove that every simple semi

Source URL: www.mat.uniroma2.it

The probability of primality of the order of a genus 2 curve Jacobian

Source URL: 2010.eccworkshop.org

Explicit Endomorphisms and Correspondences Benjamin Smith A thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy in Pure Mathematics at the University of Sydney, December 2005.

Source URL: iml.univ-mrs.fr

• Algebra
• Abstract algebra
• Geometry
• Algebraic curves
• Hyperelliptic curve
• Abelian variety
• Elliptic curve
• Complex multiplication
• Endomorphism ring
• Jacobian variety
• Ring
• Ample line bundle

A curve and its abstract Jacobian Boris Zilber University of Oxford August 22, 2012 Abstract Let C(K) be the K-points of a smooth projective curve C of genus

Source URL: people.maths.ox.ac.uk

• Mathematics
• Algebra
• Abstract algebra
• Model theory
• Algebraic varieties
• Functions and mappings
• Algebraic curves
• Morphism of algebraic varieties
• Interpretation
• Elliptic curve
• Divisor
• Strongly minimal theory

EXPLICIT KUMMER SURFACE FORMULAS FOR ARBITRARY CHARACTERISTIC ¨ JAN STEFFEN MULLER Abstract. If C is a curve of genus 2 defined over a field k and J is its Jacobian, then we can associate a hypersurface K in P3 to J,

Source URL: www.math.uni-hamburg.de

Computing canonical heights using arithmetic intersection theory We show how the canonical height on the Jacobian of a smooth projective curve over a number field can be computed in practice using arithmetic intersection

Source URL: www.uni-regensburg.de

Double-and-Add with Relative Jacobian Coordinates Björn Fay December 20, 2014 Abstract

Source URL: eprint.iacr.org

• Numerical software
• Elliptic curve cryptography
• Elliptic curves

Novel Precomputation Schemes for Elliptic Curve Cryptosystems Patrick Longa, and Catherine Gebotys Department of Electrical and Computer Engineering University of Waterloo, Canada {plonga, cgebotys}@uwaterloo.ca

Source URL: eprint.iacr.org

• Elliptic curves
• Finite fields
• Analytic number theory
• Elliptic curve
• Group theory
• Edwards curve
• Inversive geometry
• Hessian form of an elliptic curve
• Jacobian curve
• Abstract algebra
• Cryptography
• Elliptic curve cryptography

Satake compactications, Lattices and Schottky problem Giulio Codogni University of Cambridge Selwyn College

Source URL: ricerca.mat.uniroma3.it

• Algebraic curves
• Moduli theory
• Abelian varieties
• Riemann surfaces
• Schottky problem
• Modular form
• Hyperelliptic curve
• Moduli space
• Jacobian variety
• Algebraic geometry
• Abstract algebra
• Geometry

CONSTRUCTING PAIRING-FRIENDLY HYPERELLIPTIC CURVES USING WEIL RESTRICTION DAVID MANDELL FREEMAN1 AND TAKAKAZU SATOH2 Abstract. A pairing-friendly curve is a curve over a finite field whose Jacobian has small embedding de

Source URL: theory.stanford.edu

• Algebraic curves
• Algebraic surfaces
• Elliptic curves
• Analytic number theory
• Abelian varieties
• Isogeny
• Hyperelliptic curve
• Supersingular elliptic curve
• Weil restriction
• Algebraic geometry
• Abstract algebra
• Geometry