Galois representations and Galois groups over Q

Arias de Reyna Domínguez, SaraArmana, CécileKaremaker, ValentijnRebolledo, MarusiaThomas, LaraVila Oliva, NúriaBertin, Marie JoséBucur, AlinaFeigon, BrookeSchneps, Leila2016-11-112016-11-112015978331917986597833191798722364-5733http://hdl.handle.net/11441/48457In 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].application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Galois representations and Galois groups over Qinfo:eu-repo/semantics/bookPartinfo:eu-repo/semantics/openAccesshttps://doi.org/10.1007/978-3-319-17987-2_8