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Browsing by Author "Arias de Reyna Domínguez, Sara"
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Abelian varieties over number fields, tame ramification and big Galois image [Article]
Arias de Reyna Domínguez, Sara; Kappen, Christian (International Press, 2013)Given a natural number n ≥ 1 and a number field K, we show the existence of an integer ℓ0 such that for any prime number ℓ ≥ ℓ0, there exists a finite extension F/K, unramified in all places above ℓ, together with a ...

Big monodromy theorem for abelian varieties over finitely generated fields [Article]
Arias de Reyna Domínguez, Sara; Gajda, Wojciech J.; Petersen, Sebastian (Elsevier, 201302)An abelian variety over a field K is said to have big monodromy, if the image of the Galois representation on ℓtorsion points, for almost all primes ℓ, contains the full symplectic group. We prove that all abelian varieties ...

Cálculo explícito de Elementos de Frobenius en Grupos de Galois [Final Degree Work]
Garrido López, Verónica (2019)In the XIX century David Hilbert proposed a problem in Galois Theory that remains unanswered today, “Every finite group appears as the Galois group of some Galois extension of the rational numbers” A related question ...

Classification of subgroups of symplectic groups over finite fields containing a transvection [Article]
Arias de Reyna Domínguez, Sara; Dieulefait, Luis Víctor; Wiese, Gabor (De Gruyter Open, 201606)In this note, we give a selfcontained proof of the following classification (up to conjugation) of finite subgroups of GSpnpF`q containing a nontrivial transvection for ≥ 5, which can be derived from work of Kantor: G ...

Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations [Article]
Arias de Reyna Domínguez, Sara; Dieulefait, Luis Víctor; Wiese, Gabor (American Mathematical Society, 201702)This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field ...

Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image [Article]
Arias de Reyna Domínguez, Sara; Dieulefait, Luis Víctor; Wiese, Gabor (Mathematical Sciences Publishers, 201603)This article is the second part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part is concerned with symplectic Galois ...

Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties [Article]
Arias de Reyna Domínguez, Sara; Dieulefait, Luis Víctor; Shin, Sug Woo; Wiese, Gabor (Springer, 201504)This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result ...

Formal groups, supersingular abelian varieties and tame ramification [Article]
Arias de Reyna Domínguez, Sara (Elsevier, 20110515)Let us consider an abelian variety defined over Qℓ with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the ℓtorsion points of the variety ...

Galois representations and Galois groups over Q [Chapter of Book]
Arias de Reyna Domínguez, Sara; Armana, Cécile; Karemaker, Valentijn; Rebolledo, Marusia; Thomas, Lara; Vila Oliva, Núria (Springer, 2015)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 ...

Large Galois images for Jacobian varieties of genus 3 curves [Article]
Arias de Reyna Domínguez, Sara; Armana, Cécile; Karemaker, Valentijn; Rebolledo, Marusia; Thomas, Lara; Vila Oliva, Núria (Polish Academy of Sciences, Institute of Mathematics, 2016)Given a prime number ℓ ≥ 5, we construct an infinite family of threedimensional abelian varieties over Q such that, for any A/Q in the family, the Galois representation ρA,ℓ : GQ → GSp6 (Fℓ) attached to the ℓtorsion of ...

On conjectures of SatoTate and BruinierKohnen [Article]
Arias de Reyna Domínguez, Sara; Inam, Ilker; Wiese, Gabor (Springer, 201504)This article covers three topics. (1) It establishes links between the density of certain subsets of the set of primes and related subsets of the set of natural numbers. (2) It extends previous results on a conjecture of ...

Spaces of modular forms. Modular curves and dimensions [Master's Thesis]
López Sánchez, Jesús (20190620)The Modularity Theorem states that all rational elliptic curve arise from modular forms. In 1995, Andrew Wiles proved a special case of this theorem (then known as the Taniyama–Shimura conjecture) for semistable elliptic ...

Tame Galois realizations of GSp4 (Fℓ) over Q [Article]
Arias de Reyna Domínguez, Sara; Vila Oliva, Núria (Oxford University Press, 2011)In this paper we obtain realizations of the 4dimensional general symplectic group over a prime field of characteristic ℓ > 3 as the Galois group of a tamely ramified Galois extension of Q. The strategy is to consider ...