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Galois representations and Galois groups over Q

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 ρ¯ℓ: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 ρ¯ℓ is surjective. In particular we realize GSp6(Fℓ)as a Galois group over Q for all primes ℓ ∈ [11,500,000]
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Contributor : Cécile Armana Connect in order to contact the contributor
Submitted on : Thursday, February 17, 2022 - 3:10:45 PM
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Sara Arias-De-Reyna, Cécile Armana, Valentijn Karemaker, Marusia Rebolledo, Lara Thomas, et al.. Galois representations and Galois groups over Q. Women in Numbers Europe; Research Directions in Number Theory, Springer International Publishing, 2015, Association for Women in Mathematics Series, 978-3-319-17987-2. ⟨10.1007/978-3-319-17987-2_8⟩. ⟨hal-01037959⟩



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