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Large Galois images for Jacobian varieties of genus 3 curves Arias de Reyna Dominguez, Sara ; ; et al in Acta Arithmetica (2016), 174 Detailed reference viewed: 35 (0 UL)Large Galois images for Jacobian varieties of genus 3 curves Arias De Reyna Dominguez, Sara ; ; et al E-print/Working paper (2015) Given a prime number l greater than or equal to 5, we construct an infinite family of three-dimensional abelian varieties over Q such that, for any A/Q in the family, the Galois representation \rho_{A, l ... [more ▼] Given a prime number l greater than or equal to 5, we construct an infinite family of three-dimensional abelian varieties over Q such that, for any A/Q in the family, the Galois representation \rho_{A, l}: Gal_Q -> GSp(6, l) attached to the l-torsion of A is surjective. Any such variety A will be the Jacobian of a genus 3 curve over Q whose respective reductions at two auxiliary primes we prescribe to provide us with generators of Sp(6, l). [less ▲] Detailed reference viewed: 53 (1 UL)Galois representations and Galois groups over Q Arias De Reyna Dominguez, Sara ; ; et al in Bertin, Marie José; Bucur, Alina; Feigon, Brooke (Eds.) et al Women in Numbers Europe Research Directions in Number Theory (2015) In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve and let J(C) be the associated Jacobian variety. Assume that ... [more ▼] In this paper we generalize results of P. Le Duff to genus n hyperelliptic curves. More precisely, let C/Q be a hyperelliptic genus n curve and let J(C) be the associated Jacobian variety. Assume that there exists a prime p such that J(C) has semistable reduction with toric dimension 1 at p. We provide an algorithm to compute a list of primes l (if they exist) such that the Galois representation attached to the l-torsion of J(C) is surjective onto the group GSp(2n, l). In particular we realize GSp(6, l) as a Galois group over Q for all primes l in [11, 500000]. [less ▲] Detailed reference viewed: 59 (9 UL) |
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