Galois Representations and Galois Groups Over Q
Publication date
2015
Authors
Arias-de-Reyna, Sara
Armana, Cécile
Karemaker, Valentijn
Rebolledo, Marusia
Thomas, Lara
Vila, Núria
Editors
Bertin, Marie José
Bucur, Alina
Feigon, Brooke
Schneps, Leila
Advisors
Supervisors
Document Type
Part of book
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Abstract
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 N` W GQ ! GSp.J.C/OE`/ be the Galois representation attached to the `-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 ` (if they exist) such that N` is surjective. In particular we realize GSp6.F`/ as a Galois group over Q for all primes ` 2 OE11; 500;000.
Keywords
Abelian Variety, Characteristic Polynomial, Galois Group, Galois Representation, Modular Form, Taverne, General Mathematics, Gender Studies
Citation
Arias-de-Reyna, S, Armana, C, Karemaker, V, Rebolledo, M, Thomas, L & Vila, N 2015, Galois Representations and Galois Groups Over Q. in M J Bertin, A Bucur, B Feigon & L Schneps (eds), Women in Numbers Europe : Research Directions in Number Theory. 1 edn, Association for Women in Mathematics Series, vol. 2, Springer, pp. 191-205. https://doi.org/10.1007/978-3-319-17987-2_8