Linearizing torsion classes in the Picard group of algebraic curves over finite fields

Abstract

We address the problem of computing in the group of ${\ell }^k$-torsion rational points of the jacobian variety of algebraic curves over finite fields, with a view toward computing modular representations.

To appear in Journal of Algebra

References in corpus (1)

• On the computation of Galois representations associated to level one modular forms

Cited by in corpus (5)

• Computing endomorphism rings of elliptic curves under the GRH
• Translating the discrete logarithm problem on Jacobians of genus 3 hyperelliptic curves with $(\ell ,\ell ,\ell )$-isogenies
• Descent on elliptic surfaces and arithmetic bounds for the Mordell-Weil rank
• Constructing Picard curves with complex multiplication using the Chinese Remainder Theorem
• A faster pseudo-primality test