Tame Galois realizations of GSp_4(F_l) over Q

Autor:	Arias-de-Reyna, Sara, Vila, Núria
Rok vydání:	2009
Předmět:	Mathematics - Number Theory 12F12 11F80 11G30 11R32
Druh dokumentu:	Working Paper
Popis:	In this paper we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic $\ell>3$ as the Galois group of a tamely ramified Galois extension of $\mathbb{Q}$. The strategy is to consider the Galois representation $\rho_{\ell}$ attached to the Tate module at $\ell$ of a suitable abelian surface. We need to choose the abelian varieties carefully in order to ensure that the image of $\rho_{\ell}$ 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 $\ell$-torsion points of their Jacobian varieties provide tame Galois realizations of the desired symplectic groups. Comment: 29 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/0910.1445 Zobrazit plný text záznamu View this record from Arxiv