Kolyvagin’s result on the vanishing of Ш(E/K)[p ] and its consequences for anticyclotomic Iwasawa theory
Journal de théorie des nombres de Bordeaux, Tome 31 (2019) no. 2, pp. 455-501.

We discuss improvements of Kolyvagin’s classical result about the vanishing of the p-primary part of the Tate–Šafarevič group of an elliptic curve E (defined over ) over an imaginary quadratic field K satisfying the Heegner hypothesis for which the basic Heegner point y K E(K) is not divisible by an odd prime p. Combining Kolyvagin’s theorem with a new abstract Iwasawa-theoretical result, we deduce, under suitable assumptions, that similar vanishing holds for all layers in the anticyclotomic Z p -extension of K.

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DOI : 10.5802/jtnb.1091
Classification : 11G05, 11G18, 11G40, 14G10, 14G35
Mots clés : Heegner points, elliptic curves, Iwasawa theory
Ahmed Matar 1 ; Jan Nekovář 2

1 Department of Mathematics University of Bahrain P.O. Box 32038 Sukhair, Bahrain
2 Sorbonne Université Campus Pierre et Marie Curie Institut de Mathématiques de Jussieu Théorie des Nombres, Case 247 4 place Jussieu 75252 Paris cedex 05, France
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Kolyvagin{\textquoteright}s result on the vanishing of $\protect \Sha(E/K)[p^\infty ]$ and its consequences for anticyclotomic {Iwasawa} theory},
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Ahmed Matar; Jan Nekovář. Kolyvagin’s result on the vanishing of $\protect \Sha(E/K)[p^\infty ]$ and its consequences for anticyclotomic Iwasawa theory. Journal de théorie des nombres de Bordeaux, Tome 31 (2019) no. 2, pp. 455-501. doi : 10.5802/jtnb.1091. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1091/

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