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 : https://doi.org/10.5802/jtnb.1091
Classification : 11G05,  11G18,  11G40,  14G10,  14G35
Mots clés : Heegner points, elliptic curves, Iwasawa theory
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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},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
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Matar, Ahmed; Nekovář, Jan. 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. http://archive.numdam.org/articles/10.5802/jtnb.1091/

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