Weil-Ch\^atelet divisible elements in Tate-Shafarevich groups I: The Bashmakov problem for elliptic curves over Q

Jakob Stix; Mirela \c{C}iperiani

arxiv: 1106.4255 · v2 · pith:76OP7424new · submitted 2011-06-21 · 🧮 math.NT

Weil-Ch\^atelet divisible elements in Tate-Shafarevich groups I: The Bashmakov problem for elliptic curves over Q

Mirela \c{C}iperiani , Jakob Stix This is my paper

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keywords curvesellipticsubgroupabelianateletbashmakovcompletediscuss

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For an abelian variety A over a number field k we discuss the maximal divisibile subgroup of H^1(k,A) and its intersection with the subgroup Sha(A/k). The results are most complete for elliptic curves over Q.

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Weil-Ch\^atelet divisible elements in Tate-Shafarevich groups I: The Bashmakov problem for elliptic curves over Q

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