Kolyvagin’s result on the vanishing of Ш(E/K)[p ] and its consequences for anticyclotomic Iwasawa theory
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Journal de Théorie des Nombres de Bordeaux, Volume 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.

Received : 2018-11-20
Accepted : 2019-07-15
Published online : 2019-10-29
DOI : https://doi.org/10.5802/jtnb.1091
Classification:  11G05,  11G18,  11G40,  14G10,  14G35
Keywords: Heegner points, elliptic curves, Iwasawa theory
@article{JTNB_2019__31_2_455_0,
     author = {Ahmed Matar and Jan Nekov\'a\v r},
     title = {Kolyvagin'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},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {31},
     number = {2},
     year = {2019},
     pages = {455-501},
     doi = {10.5802/jtnb.1091},
     language = {en},
     url={jtnb.centre-mersenne.org/item/JTNB_2019__31_2_455_0/}
}
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, Volume 31 (2019) no. 2, pp. 455-501. doi : 10.5802/jtnb.1091. https://jtnb.centre-mersenne.org/item/JTNB_2019__31_2_455_0/

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