Torsion groups of elliptic curves over quadratic fields
Torsion points in families of Drinfeld modules
Let be an algebraic family of Drinfeld modules defined over a field K of characteristic p, and let a,b ∈ K[λ]. Assume that neither a(λ) nor b(λ) is a torsion point for for all λ. If there exist infinitely many λ ∈ K̅ such that both a(λ) and b(λ) are torsion points for , then we show that for each λ ∈ K̅, a(λ) is torsion for if and only if b(λ) is torsion for . In the case a,b ∈ K, we prove in addition that a and b must be -linearly dependent.
Torsion points on abelian varieties of CM-type
Torsion points on elliptic curves and galois module structure.
Torsion points on elliptic curves and q-coeffincients of modular forms.
Torsion points on families of simple abelian surfaces and Pell's equation over polynomial rings (with an appendix by E. V. Flynn)
In recent papers we proved a special case of a variant of Pink’s Conjecture for a variety inside a semiabelian scheme: namely for any curve inside anything isogenous to a product of two elliptic schemes. Here we go beyond the elliptic situation by settling the crucial case of any simple abelian surface scheme defined over the field of algebraic numbers, thus confirming an earlier conjecture of Shou-Wu Zhang. This is of particular relevance in the topic, also in view of very recent counterexamples...
Torsion subgroups of elliptic curves with non-cyclic torsion over ℚ in elementary abelian 2-extensions of ℚ
Torsors under tori and Néron models
Let be a Henselian discrete valuation ring with field of fractions . If is a smooth variety over and a torus over , then we consider -torsors under . If is a model of then, using a result of Brahm, we show that -torsors under extend to -torsors under a Néron model of if is split by a tamely ramified extension of . It follows that the evaluation map associated to such a torsor factors through reduction to the special fibre. In this way we can use the geometry of the special...
Traces of high powers of the Frobenius class in the hyperelliptic ensemble
Transcendence and Drinfeld modules.
Transformation de Fourier homogène
Dans leur démonstration de la correspondance de Drinfeld-Langlands, Frenkel, Gaitsgory et Vilonen utilisent la transformation de Fourier géométrique, ce qui les oblige à travailler soit avec les faisceaux -adiques en caractéristique , soit avec les -Modules en caractéristique . En fait, ils n’utilisent cette transformation de Fourier géométrique que pour des faisceaux homogènes pour lesquels on s’attend à avoir une transformation de Fourier sur . L’objet de cette note est de proposer une telle...
Travaux de Frenkel, Gaitsgory et Vilonen sur la correspondance de Drinfeld-Langlands
Travaux de Kolyvagin et Rubin
Travaux de Shimura et Taniyama sur la multiplication complexe
Travaux de Wiles (et Taylor, ...), partie I
Travaux de Wiles (et Taylor, ...), partie II
Traverso’s Isogeny Conjecture for -Divisible Groups
Triples of Positive Integers with the same Sum and the same Product
It is proved that for every k there exist k triples of positive integers with the same sum and the same product.
Trivial points on towers of curves
In order to study the behavior of the points in a tower of curves, we introduce and study trivial points on towers of curves, and we discuss their finiteness over number fields. We relate the problem of proving that the only rational points are the trivial ones at some level of the tower, to the unboundeness of the gonality of the curves in the tower, which we show under some hypothesis.
Trivial Selmer groups and even partitions of a graph.