AbstractWe show that the p-torsion in the Tate–Shafarevich group of any principally polarized abelian variety over a number field is unbounded as one ranges over extensions of degree O(p), the implied constant depending only on the dimension of the abelian variety
Let A be an abelian variety defined over a number field K. It is proved that for the composite field...
Let (A, ë) be a principally polarized abelian variety defined over a global field k, and let ..(A) b...
We consider a simple principally polarized abelian variety A of dimension g defined over a number fi...
AbstractWe show that the p-torsion in the Tate–Shafarevich group of any principally polarized abelia...
26 pagesLet A be an abelian variety of dimension g defined over a number field K. We study the size ...
Fix an integer d\u3e0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic cu...
Let $A$ be an abelian variety over a $p$-adic field $K$ and $L$ an algebraic infinite extension over...
AbstractWe prove: Let A be an abelian variety over a number field K. Then K has a finite Galois exte...
We give a uniform bound on the degree of the maximal torsion cosets for subvarieties of an abelian v...
An elliptic curve defined over a number field K => Q, where [K: Q] < oo, is an abelian variety...
Le théorème de Mordell-Weil affirme que, pour toute variété abélienne définie sur un corps de nombre...
17 pages; final version, to appear in Compositio MathematicaInternational audienceLet $A$ be an abel...
19 pages; final version, to appear in Journal of the London Mathematical SocietyInternational audien...
We show that, for any d, the 2-torsion of Tate-Shafarevich groups of absolutely simple abelian varie...
In this paper we are motivated by the following problem: Let A/K be an abelian variety defined over ...
Let A be an abelian variety defined over a number field K. It is proved that for the composite field...
Let (A, ë) be a principally polarized abelian variety defined over a global field k, and let ..(A) b...
We consider a simple principally polarized abelian variety A of dimension g defined over a number fi...
AbstractWe show that the p-torsion in the Tate–Shafarevich group of any principally polarized abelia...
26 pagesLet A be an abelian variety of dimension g defined over a number field K. We study the size ...
Fix an integer d\u3e0. In 2008, Chantal David and Tom Weston showed that, on average, an elliptic cu...
Let $A$ be an abelian variety over a $p$-adic field $K$ and $L$ an algebraic infinite extension over...
AbstractWe prove: Let A be an abelian variety over a number field K. Then K has a finite Galois exte...
We give a uniform bound on the degree of the maximal torsion cosets for subvarieties of an abelian v...
An elliptic curve defined over a number field K => Q, where [K: Q] < oo, is an abelian variety...
Le théorème de Mordell-Weil affirme que, pour toute variété abélienne définie sur un corps de nombre...
17 pages; final version, to appear in Compositio MathematicaInternational audienceLet $A$ be an abel...
19 pages; final version, to appear in Journal of the London Mathematical SocietyInternational audien...
We show that, for any d, the 2-torsion of Tate-Shafarevich groups of absolutely simple abelian varie...
In this paper we are motivated by the following problem: Let A/K be an abelian variety defined over ...
Let A be an abelian variety defined over a number field K. It is proved that for the composite field...
Let (A, ë) be a principally polarized abelian variety defined over a global field k, and let ..(A) b...
We consider a simple principally polarized abelian variety A of dimension g defined over a number fi...
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