Large Galois images for Jacobian varieties of genus 3 curve
Cécile Armana ( Université de Franche-Comté (UFR Sciences et techniques) , France )
2016-04-15 10:30 - 11:30
Room 103, Mathematics Research Center Building (ori. New Math. Bldg.)
Let l be a prime number and A a principally polarized abelian variety of dimension n over Q. One can attach to the l-torsion of A a Galois representation of the absolute Galois group of Q which takes values in the symplectic group GSp(2n)(F_l). Under certain hypotheses on A, it is known that this representation is surjective (see Serre, Hall,...). In this talk we will fix a prime number l, greater than or equal to 5, and present a construction of an infinite family of 3-dimensional abelian varieties over Q such that the Galois representation attached to any abelian variety in this family is surjective. These varieties will be Jacobians of genus 3 curves over Q with prescribed reductions at auxiliary primes. This is joint work with S. Arias-de-Reyna, V. Karemaker, M. Rebolledo, L. Thomas and N. Vila.