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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)Tame Galois realizations of $ GSp_4(\Bbb F_łl)$ over $\Bbb Q$ Arias De Reyna Dominguez, Sara ; in International Mathematics Research Notices (2011), (9), 2028--2046 In this paper, we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic l> 3 as the Galois group of a tamely ramified Galois extension of Q. The strategy ... [more ▼] In this paper, we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic l> 3 as the Galois group of a tamely ramified Galois extension of Q. The strategy is to consider the Galois representation ρ_l attached to the Tate module at l of a suitable abelian surface. We need to choose the abelian surfaces carefully in order to ensure that the image of ρ_l is large and simultaneously maintain a control on the ramification of the corresponding Galois extension. We obtain an explicit family of curves of genus 2 such that the Galois representation attached to the l-torsion points of their Jacobian varieties provides tame Galois realizations of the desired symplectic groups. [less ▲] Detailed reference viewed: 52 (0 UL)Galois representations and the tame inverse Galois problem Arias De Reyna Dominguez, Sara ; in Cojocaru, Alina-Carmen; Lauter, Kristin; Pries, Rachel (Eds.) et al WIN---women in numbers (2011) In this paper we will focus on a variant of the Inverse Galois Problem over the rationals, emphasizing the progress made through the analysis of the Galois representations arising from arithmetic ... [more ▼] In this paper we will focus on a variant of the Inverse Galois Problem over the rationals, emphasizing the progress made through the analysis of the Galois representations arising from arithmetic-geometric objects. [less ▲] Detailed reference viewed: 76 (1 UL)Tame Galois realizations of $ GL_2(\Bbb F_l)$ over $\Bbb Q$ Arias De Reyna Dominguez, Sara ; in Journal of Number Theory (2009), 129(5), 1056--1065 This paper concerns the tame inverse Galois problem. For each prime number l, we construct infinitely many semistable elliptic curves over Q with good supersingular reduction at l. The Galois action on ... [more ▼] This paper concerns the tame inverse Galois problem. For each prime number l, we construct infinitely many semistable elliptic curves over Q with good supersingular reduction at l. The Galois action on the l-torsion points of these elliptic curves provides tame Galois realizations of GL_2(F_l) over Q. [less ▲] Detailed reference viewed: 25 (2 UL) |
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