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El grupo cuspidal Arias De Reyna Dominguez, Sara Presentation (2014, January 30) Detailed reference viewed: 22 (0 UL)Galois representations and Galois groups over Q Arias De Reyna Dominguez, Sara Scientific Conference (2013, October 14) Detailed reference viewed: 28 (2 UL)Abelian varieties with tame and surjective Galois representations Arias De Reyna Dominguez, Sara Scientific Conference (2013, August) Detailed reference viewed: 30 (3 UL)Automorphic Galois representations and the inverse Galois problem Arias De Reyna Dominguez, Sara Scientific Conference (2013, July 09) Detailed reference viewed: 64 (2 UL)Abelian varieties over number fields, tame ramification and big Galois image Arias De Reyna Dominguez, Sara ; in Mathematical Research Letters (2013), 20(01), 1-17 Given a natural number n ≥ 1 and a number field K, we show the existence of an integer l_0 such that for any prime number l ≥ l_0 , there exists a finite extension F/K, unramified in all places above l ... [more ▼] Given a natural number n ≥ 1 and a number field K, we show the existence of an integer l_0 such that for any prime number l ≥ l_0 , there exists a finite extension F/K, unramified in all places above l, together with a principally polarized abelian variety A of dimension n over F such that the resulting l-torsion representation ρ_{A,l} : G_F → GSp(A[l]) is surjective and everywhere tamely ramified. In particular, we realize GSp_{2n}(F_l) as the Galois group of a finite tame extension of number fields F' /F such that F is unramified above l. [less ▲] Detailed reference viewed: 78 (0 UL)Winter School on Galois Theory, Volume 2 Wiese, Gabor ; Arias De Reyna Dominguez, Sara ; Book published by University of Luxembourg / Campus Kirchberg (2013) Galois Theory plays a key role in many mathematical disciplines, such as number theory, algebra, topology, and geometry. This special volume of the Luxembourg based peer-reviewed mathematics journal ... [more ▼] Galois Theory plays a key role in many mathematical disciplines, such as number theory, algebra, topology, and geometry. This special volume of the Luxembourg based peer-reviewed mathematics journal "Travaux mathématiques" unites four instructional texts that have grown out of lectures delivered at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. It also includes one research article. Gebhard Böckle's contribution is a quite comprehensive survey on Galois representations. It focusses on the key ideas, and the long list of recommended references enables the reader to pursue himself/herself any of the mentioned topics in greater depth. Michael Schein's notes sketch the proof due to Khare and Wintenberger of one of the major theorems in arithmetic algebraic geometry in recent years, namely Serre's Modularity Conjecture. Moshe Jarden's contribution is based on his book on algebraic patching. It develops the method of algebraic patching from scratch and gives applications in contemporary Galois theory. David Harbater's text is complementary to Jarden's notes, and describes recent applications of patching in other aspects of algebra, for example: differential algebra, local-global principles, quadratic forms, and more. The focus is on the big picture and on providing the reader with intuition. The research article by Wulf-Dieter Geyer and Moshe Jarden concerns model completeness of valued PAC fields. [less ▲] Detailed reference viewed: 167 (10 UL)Big monodromy theorem for abelian varieties over finitely generated fields Arias De Reyna Dominguez, Sara ; ; in Journal of Pure and Applied Algebra (2013), 217(2), 218--229 An abelian variety over a field K is said to have big monodromy, if the image of the Galois representation on l-torsion points, for almost all primes l contains the full symplectic group. We prove that ... [more ▼] An abelian variety over a field K is said to have big monodromy, if the image of the Galois representation on l-torsion points, for almost all primes l contains the full symplectic group. We prove that all abelian varieties over a finitely generated field K with the endomorphism ring Z and semistable reduction of toric dimension one at a place of the base field K have big monodromy. We make no assumption on the transcendence degree or on the characteristic of K. This generalizes a recent result of Chris Hall. [less ▲] Detailed reference viewed: 75 (0 UL)Winter School on Galois Theory, Volume 1 Wiese, Gabor ; Arias De Reyna Dominguez, Sara ; Book published by University of Luxembourg / Campus Kirchberg (2013) Galois Theory plays a key role in many mathematical disciplines, such as number theory, algebra, topology, and geometry. This special volume of the Luxembourg based peer-reviewed mathematics journal ... [more ▼] Galois Theory plays a key role in many mathematical disciplines, such as number theory, algebra, topology, and geometry. This special volume of the Luxembourg based peer-reviewed mathematics journal "Travaux mathématiques" unites two instructional texts that have grown out of lectures delivered at the Winter School on Galois Theory held at the University of Luxembourg in February 2012. The contribution by Wulf-Dieter Geyer is about "Field Theory". It can be considered as a textbook in its own right. It manages to start at the level that any student possesses after any introductory algebra course and nevertheless to lead the reader to very advanced field theory at the frontier of current research, and to cover a wealth of material. Many examples are contained, which nicely enlighten the presented concepts, very often providing counterexamples that show why certain hypotheses are necessary. One also finds a chapter on the history of field theory as well as other historical remarks throughout the text. The second contribution addresses "Profinite Groups". It is written by Luis Ribes, who is the author of two standard books on this subject. Being necessarily much shorter than the two books, it has the feature of presenting an overview stressing the main concepts and the links with Galois Theory. Since for those proofs which are not included precise references are given, the notes, due to their conciseness and nevertheless great amount of material, constitute an excellent starting point for any Master or PhD student willing to learn this subject. [less ▲] Detailed reference viewed: 201 (20 UL)Abelian varieties over finitely generated fields and the conjecture of Geyer and Jarden on torsion Arias De Reyna Dominguez, Sara ; ; in Mathematische Nachrichten (2013), 286(13), 1269-1286 In this paper we prove the Geyer-Jarden conjecture on the torsion part of the Mordell-Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic ... [more ▼] In this paper we prove the Geyer-Jarden conjecture on the torsion part of the Mordell-Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic. The class consists of all abelian varieties with big monodromy, i.e., such that the image of Galois representation on l-torsion points, for almost all primes l, contains the full symplectic group. [less ▲] Detailed reference viewed: 73 (2 UL)Algebra 3 Arias De Reyna Dominguez, Sara Learning material (2013) These lecture notes correspond to the course Algebra 3 from the Bachelor en Sciences et Ingénierie, Filière mathématiques, of the University of Luxembourg. This course was taught in the Winter Term 2013 ... [more ▼] These lecture notes correspond to the course Algebra 3 from the Bachelor en Sciences et Ingénierie, Filière mathématiques, of the University of Luxembourg. This course was taught in the Winter Term 2013 and it consists of 14 lectures of 90 minutes each. This lecture belongs to the third semester of the Bachelor, and it builds on the lectures Algebra 1 and Algebra 2, belonging to the first and second semester respectively. The aim of this course is to introduce the students to the theory of algebraic extensions of fields, and culminates with the application of the theory to the solution (negative solution, in fact) of the three classical Greek problems concerning constructions with ruler and compass. This lecture is also a preliminary step towards Galois theory, which is taught in the fourth semester of the Bachelor. [less ▲] Detailed reference viewed: 134 (2 UL)Compatible systems of symplectic Galois representations with large residual image Arias De Reyna Dominguez, Sara Scientific Conference (2012, June 29) Detailed reference viewed: 15 (0 UL)Compatible systems of symplectic Galois representations with large residual image Arias De Reyna Dominguez, Sara Scientific Conference (2012, June) Detailed reference viewed: 22 (0 UL)On a conjecture of Geyer and Jarden about abelian varieties over finitely generated fields Arias De Reyna Dominguez, Sara Scientific Conference (2011, September 05) Detailed reference viewed: 20 (0 UL)Formal groups, supersingular abelian varieties and tame ramification Arias De Reyna Dominguez, Sara in Journal of Algebra (2011), 334 Let us consider an abelian variety defined over the field of l-adic numbers with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia ... [more ▼] Let us consider an abelian variety defined over the field of l-adic numbers with good supersingular reduction. In this paper we give explicit conditions that ensure that the action of the wild inertia group on the l-torsion points of the variety is trivial. Furthermore we give a family of curves of genus 2 such that their Jacobian surfaces have good supersingular reduction and satisfy these conditions. We address this question by means of a detailed study of the formal group law attached to abelian varieties. [less ▲] Detailed reference viewed: 95 (0 UL)Tame Galois realizations of $ GSp_4(\Bbb F_łl)$ over $\Bbb Q$ Arias De Reyna Dominguez, Sara ; in International Mathematics Research Notices (2011), (9), 2028--2046 In this paper, we obtain realizations of the 4-dimensional 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 ... [more ▼] In this paper, we obtain realizations of the 4-dimensional 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 the Galois representation ρ_l attached to the Tate module at l of a suitable abelian surface. We need to choose the abelian surfaces carefully in order to ensure that the image of ρ_l is large and simultaneously maintain a control on the ramification of the corresponding Galois extension. We obtain an explicit family of curves of genus 2 such that the Galois representation attached to the l-torsion points of their Jacobian varieties provides tame Galois realizations of the desired symplectic groups. [less ▲] Detailed reference viewed: 81 (0 UL)Galois representations and the tame inverse Galois problem Arias De Reyna Dominguez, Sara ; in Cojocaru, Alina-Carmen; Lauter, Kristin; Pries, Rachel (Eds.) et al WIN---women in numbers (2011) In this paper we will focus on a variant of the Inverse Galois Problem over the rationals, emphasizing the progress made through the analysis of the Galois representations arising from arithmetic ... [more ▼] In this paper we will focus on a variant of the Inverse Galois Problem over the rationals, emphasizing the progress made through the analysis of the Galois representations arising from arithmetic-geometric objects. [less ▲] Detailed reference viewed: 113 (1 UL)Tame Galois realizations of $ GL_2(\Bbb F_l)$ over $\Bbb Q$ Arias De Reyna Dominguez, Sara ; in Journal of Number Theory (2009), 129(5), 1056--1065 This paper concerns the tame inverse Galois problem. For each prime number l, we construct infinitely many semistable elliptic curves over Q with good supersingular reduction at l. The Galois action on ... [more ▼] This paper concerns the tame inverse Galois problem. For each prime number l, we construct infinitely many semistable elliptic curves over Q with good supersingular reduction at l. The Galois action on the l-torsion points of these elliptic curves provides tame Galois realizations of GL_2(F_l) over Q. [less ▲] Detailed reference viewed: 31 (2 UL) |
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