Chapter of Book
Galois representations and Galois groups over Q
Author/s | Arias de Reyna Domínguez, Sara
Armana, Cécile Karemaker, Valentijn Rebolledo, Marusia Thomas, Lara Vila Oliva, Núria |
Editor | Bertin, Marie José
Bucur, Alina Feigon, Brooke Schneps, Leila |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2015 |
Deposit Date | 2016-11-11 |
Published in |
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ISBN/ISSN | 9783319179865 9783319179872 2364-5733 |
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 ¯ρℓ : GQ → GSp(J(C)[ℓ]) be ... 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 ¯ρℓ : GQ → 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 ¯ρℓ is surjective. In particular we realize GSp6 (Fℓ) as a Galois group over Q for all primes ℓ ∈ [11, 500000]. |
Project ID. | MTM2012-33830
BQR 2013 ANR-12-BS01-0002 |
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