Torsion groups of elliptic curves over quadratic fields
Torsion groups of elliptic curves with integral j-invariant over quadratic fields.
Torsion p-adic Galois representations and a conjecture of Fontaine
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 curves and common divisors of and
Torsion points on elliptic curves and galois module structure.
Torsion points on elliptic curves and q-coeffincients of modular forms.
Torsion points on elliptic curves over all quadratic fields. II
Torsion points on elliptic curves over fileds of low degree.
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...
Total positivity and algebraic Witt classes.
Totale Normenreste, die keine Normen sind, als Erzeuger nichtabelscher Körpererweiterungen. II.
Totale Normenreste, die keine Normen sind, als Erzeuger nichtabelscher Körpererweiterungen. I.
Totally Brown subsets of the Golomb space and the Kirch space
A topological space is totally Brown if for each and every nonempty open subsets of we have . Totally Brown spaces are connected. In this paper we consider the Golomb topology on the set of natural numbers, as well as the Kirch topology on . Then we examine subsets of these spaces which are totally Brown. Among other results, we characterize the arithmetic progressions which are either totally Brown or totally separated in . We also show that and are aposyndetic. Our results...
Totally indefinite Euclidean quaternion fields
We study the Euclidean property for totally indefinite quaternion fields. In particular, we establish a complete list of norm-Euclidean such fields over imaginary quadratic number fields. This enables us to exhibit an example which gives a negative answer to a question asked by Eichler. The proofs are both theoretical and algorithmic.
Totally multiplicative sequences with values ... 1 which exclude four consecutive values of 1.
Totally positive algebraic integers of small trace
Let be a totally positive algebraic integer, with the difference between its trace and its degree at most 6. We describe an algorithm for finding all such , and display the resulting list of 1314 values of which the algorithm produces.