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Weil–Châtelet divisible elements in Tate–Shafarevich groups II: On a question of Cassels
-
Mirela Çiperiani
und
Jakob Stix
Veröffentlicht/Copyright:
12. April 2013
Abstract
For an abelian variety A over a number field k we discuss the divisibility in H1(k,A) of elements of the subgroup Ш(A/k). The results are most complete for elliptic curves over ℚ.
Funding source: MATCH
Funding source: Newton Institute
Funding source: NSF
Award Identifier / Grant number: DMS-07-58362
Funding source: NSA
Award Identifier / Grant number: H98230-12-1-0208
The authors would like to thank Brian Conrad, Brendan Creutz, Wojciech Gajda, and Joseph Oesterlé for several useful discussions. The first author is also grateful to her advisor, Andrew Wiles, for introducing her to this method of thinking about the p-divisibility of the Tate–Shafarevich group.
Received: 2012-7-5
Revised: 2013-2-7
Published Online: 2013-4-12
Published in Print: 2015-3-1
© 2015 by De Gruyter
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Artikel in diesem Heft
- Frontmatter
- Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
- Rigidity and stability of Einstein metrics for quadratic curvature functionals
- On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn
- Hecke algebras associated to Λ-adic modular forms
- On a notion of exactness for reduced free products of C*-algebras
- Splitting theorems for Finsler manifolds of nonnegative Ricci curvature
- Weil–Châtelet divisible elements in Tate–Shafarevich groups II: On a question of Cassels
- General curves on algebraic surfaces
- Operator biflatness of the L1-algebras of compact quantum groups
Artikel in diesem Heft
- Frontmatter
- Geometric analysis aspects of infinite semiplanar graphs with nonnegative curvature
- Rigidity and stability of Einstein metrics for quadratic curvature functionals
- On the Morse–Sard property and level sets of Wn,1 Sobolev functions on ℝn
- Hecke algebras associated to Λ-adic modular forms
- On a notion of exactness for reduced free products of C*-algebras
- Splitting theorems for Finsler manifolds of nonnegative Ricci curvature
- Weil–Châtelet divisible elements in Tate–Shafarevich groups II: On a question of Cassels
- General curves on algebraic surfaces
- Operator biflatness of the L1-algebras of compact quantum groups
