An annihilator for the p -Selmer group by means of Heegner points

Massimo Bertolini

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1994)

  • Volume: 5, Issue: 2, page 129-140
  • ISSN: 1120-6330

Abstract

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Let E / Q be a modular elliptic curve, and let K be an imaginary quadratic field. We show that the p -Selmer group of E over certain finite anticyclotomic extensions of K , modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic Z p -extension of K . This refines in the current contest a result of [1].

How to cite

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Bertolini, Massimo. "An annihilator for the \( p \)-Selmer group by means of Heegner points." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 5.2 (1994): 129-140. <http://eudml.org/doc/244212>.

@article{Bertolini1994,
abstract = {Let \( E / Q \) be a modular elliptic curve, and let \( K \) be an imaginary quadratic field. We show that the \( p \)-Selmer group of \( E \) over certain finite anticyclotomic extensions of \( K \), modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic \( \mathbb\{Z\}\_\{p\} \)-extension of \( K \). This refines in the current contest a result of [1].},
author = {Bertolini, Massimo},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Elliptic; Curve; Annihilator; Heegner; Selmer; annihilator; anticyclotomic -extension of an imaginary quadratic field; modular elliptic curve; Heegner points; Selmer group; Iwasawa theory},
language = {eng},
month = {6},
number = {2},
pages = {129-140},
publisher = {Accademia Nazionale dei Lincei},
title = {An annihilator for the \( p \)-Selmer group by means of Heegner points},
url = {http://eudml.org/doc/244212},
volume = {5},
year = {1994},
}

TY - JOUR
AU - Bertolini, Massimo
TI - An annihilator for the \( p \)-Selmer group by means of Heegner points
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1994/6//
PB - Accademia Nazionale dei Lincei
VL - 5
IS - 2
SP - 129
EP - 140
AB - Let \( E / Q \) be a modular elliptic curve, and let \( K \) be an imaginary quadratic field. We show that the \( p \)-Selmer group of \( E \) over certain finite anticyclotomic extensions of \( K \), modulo the universal norms, is annihilated by the «characteristic ideal» of the universal norms modulo the Heegner points. We also extend this result to the anticyclotomic \( \mathbb{Z}_{p} \)-extension of \( K \). This refines in the current contest a result of [1].
LA - eng
KW - Elliptic; Curve; Annihilator; Heegner; Selmer; annihilator; anticyclotomic -extension of an imaginary quadratic field; modular elliptic curve; Heegner points; Selmer group; Iwasawa theory
UR - http://eudml.org/doc/244212
ER -

References

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  1. BERTOLINI, M., Selmer groups and Heegner points in anticyclotomic Z p -extensions. Preprint. Zbl0862.11043MR1351834
  2. BERTOLINI, M. - DARMON, H., Kolyvagin's descent and Mordell-Weil groups over ring class fields. Journal für die Reine und Angewandte Mathematik, 412, 1990, 63-74. Zbl0712.14008MR1079001DOI10.1515/crll.1990.412.63
  3. GROSS, B. H., Kolyvagins work on modular elliptic curves. In: Proceedings of the Durham Symposium on L -functions and Arithmetic. Cambridge Univ. Press, 1991. Zbl0743.14021MR1110395DOI10.1017/CBO9780511526053.009
  4. PERRIN-RIOU, B., Fonctions L ⁢ p -adiques Théorie dlwasawa et points de Heegner. Bull. Soc. Math. de France, 115, 1987, 399-456. Dipartimento di Matematica Università degli Studi di Pavia Via Abbiategrasso, 209 - 27100 PAVIA Zbl0664.12010MR928018

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