Weil–Châtelet divisible elements in Tate–Shafarevich groups I: The Bashmakov problem for elliptic curves over

DOI10.1112/S0010437X12000747zbMath1300.11056arXiv1106.4255MaRDI QIDQ5299338

Jakob Stix, Mirela Ciperiani

Publication date: 25 June 2013

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.4255

zbMATH Keywords

abelian varietyelliptic curveTate-Shafarevich groupSelmer groupWeil-Châtelet groupBashmakov problem

Mathematics Subject Classification ID

Elliptic curves over global fields (11G05) Abelian varieties of dimension (> 1) (11G10) Varieties over global fields (11G35)

Related Items (2)

Kolyvagin's result on the vanishing of \(\Sha(E/K)[p^\infty\) and its consequences for anticyclotomic Iwasawa theory] ⋮ Local-global questions for divisibility in commutative algebraic groups

Cites Work

• Rational points and arithmetic of fundamental groups. Evidence for the section conjecture
• The Brauer-Manin obstruction for sections of the fundamental group
• Pro-\(\ell\) branched coverings of \(P^ 1\) and higher circular \(\ell\)- units
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• Continuous étale cohomology
• Modular curves and the Eisenstein ideal
• Nonvanishing theorems for automorphic \(L\)-functions on \(\text{GL} (2)\)
• The Cassels-Tate pairing on polarized Abelian varieties
• Galois sections for abelianized fundamental groups
• Galois properties of points of finite order of elliptic curves
• On the passage from local to global in number theory
• Elliptic curves with maximal Galois action on their torsion points
• THE COHOMOLOGY OF ABELIAN VARIETIES OVER A NUMBER FIELD
• Arithmetic on Curves of Genus 1 : III. The Tate-Šafarevič and Selmer Groups
• Almost all elliptic curves are Serre curves

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