Galois Representations and Galois Groups Over Q
| Affiliation auteurs | Affiliation ok |
| Titre | Galois Representations and Galois Groups Over Q |
| Type de publication | Conference Paper |
| Year of Publication | 2015 |
| Auteurs | Arias-de-Reyna S, Armana C, Karemaker V, Rebolledo M, Thomas L, Vila N |
| Editor | Bertin MJ, Bucur A, Feigon B, Schneps L |
| Conference Name | WOMEN IN NUMBERS EUROPE: RESEARCH DIRECTIONS IN NUMBER THEORY |
| Publisher | Clay Math Inst; Microsoft Res; Natl Sci Fdn; Number Theory Fdn |
| Conference Location | GEWERBESTRASSE 11, CHAM, CH-6330, SWITZERLAND |
| ISBN Number | 978-3-319-17987-2; 978-3-319-17986-5 |
| Résumé | 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, let J(C) be the associated Jacobian variety, and let (rho) over bar (l) : G(Q) -> GSp(J(C)[l]) be the Galois representation attached to the l-torsion of J(C). 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 (rho) over bar (l) is surjective. In particular we realize GSp(6)(F-l) as a Galois group over Q for all primes l is an element of [11, 500,000]. |
| DOI | 10.1007/978-3-319-17987-2_8 |