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ORBi

Un calcul d'anneaux de déformations potentiellement Barsotti--Tate David, Agnès ; ; E-print/Working paper (2013) Detailed reference viewed: 87 (0 UL)Algèbre 1 (BASI filière mathématiques, 2013) Wiese, Gabor ; David, Agnès Learning material (2013) Lecture notes written in French from the Algebra 1 lecture in the 1st term of the Bachelor programme BASI branch Mathematics at the University of Luxembourg. The lecture starts with preliminaries on logic ... [more ▼] Lecture notes written in French from the Algebra 1 lecture in the 1st term of the Bachelor programme BASI branch Mathematics at the University of Luxembourg. The lecture starts with preliminaries on logic, sets and functions, it builds the natural numbers (almost) from the Peano axioms, then constructs the integers and the rationals. Groups and rings are introduced in that context. The most basic definitions and results from abstract linear algebra are also given. The course finishes with some basic group theory. [less ▲] Detailed reference viewed: 99 (3 UL)Critère d'irréductibilité pour les courbes elliptiques semi-stables sur un corps de nombres David, Agnès E-print/Working paper (2012) For a fixed number field and an elliptic curve defined and semistable over this number field, we consider the set of prime numbers p such that the Galois representation attached to the p-torsion points of ... [more ▼] For a fixed number field and an elliptic curve defined and semistable over this number field, we consider the set of prime numbers p such that the Galois representation attached to the p-torsion points of the elliptic curve is reducible. When the number field satisfies a certain necessary condition, we give an explicit bound, depending only on the number field and not on the semistable elliptic curve, for these primes. This generalizes previous results of Kraus. [less ▲] Detailed reference viewed: 46 (1 UL)Caractère d'isogénie et critères d'irréductibilité David, Agnès E-print/Working paper (2011) This article deals with the Galois representation attached to elliptic curves with an isogeny of prime degree over a number field. We first determine uniform criteria for the irreducibility of Galois ... [more ▼] This article deals with the Galois representation attached to elliptic curves with an isogeny of prime degree over a number field. We first determine uniform criteria for the irreducibility of Galois representations attached to elliptic curves in some infinite families, characterised by their reduction type at some fixed places of the base field. Then, we give an explicit form for a bound that appear in a theorem of Momose. Finally, we use these results to precise a previous theorem of the author about the homotheties contained in the image of the Galois representation. [less ▲] Detailed reference viewed: 64 (0 UL) |
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