On heegner points for primes of additive reduction ramifying in the base field

Daniel Kohen; Ariel Pacetti; Marc Masdeu

doi:10.1090/tran/6990

On heegner points for primes of additive reduction ramifying in the base field

Daniel Kohen, Ariel Pacetti, Marc Masdeu

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

8 Citations (Scopus)

Abstract

Let E be a rational elliptic curve and let K be an imaginary quadratic field. In this article we give a method to construct Heegner points when E has a prime bigger than 3 of additive reduction ramifying in the field K. The ideas apply to more general contexts, like constructing Darmon points attached to real quadratic fields, which is presented in the appendix.

Original language	English
Pages (from-to)	911-926
Number of pages	16
Journal	Transactions of the American Mathematical Society
Volume	370
Issue number	2
DOIs	https://doi.org/10.1090/tran/6990
Publication status	Published - Feb 2018

Keywords

Heegner points

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10.1090/tran/6990

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title = "On heegner points for primes of additive reduction ramifying in the base field",

abstract = "Let E be a rational elliptic curve and let K be an imaginary quadratic field. In this article we give a method to construct Heegner points when E has a prime bigger than 3 of additive reduction ramifying in the field K. The ideas apply to more general contexts, like constructing Darmon points attached to real quadratic fields, which is presented in the appendix.",

keywords = "Heegner points",

author = "Daniel Kohen and Ariel Pacetti and Marc Masdeu",

note = "Funding Information: Received by the editors February 1, 2016 and, in revised form, May 11, 2016. 2010 Mathematics Subject Classification. Primary 11G05; Secondary 11G40. Key words and phrases. Heegner points. The first author was partially supported by a CONICET doctoral fellowship. The second author was partially supported by CONICET PIP 2010-2012 11220090100801, ANPCyT PICT-2013-0294 and UBACyT 2014-2017-20020130100143BA. The author of the appendix was supported by EU H2020-MSCA-IF-655662. Publisher Copyright: {\textcopyright} 2017 American Mathematical Society.",

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doi = "10.1090/tran/6990",

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N2 - Let E be a rational elliptic curve and let K be an imaginary quadratic field. In this article we give a method to construct Heegner points when E has a prime bigger than 3 of additive reduction ramifying in the field K. The ideas apply to more general contexts, like constructing Darmon points attached to real quadratic fields, which is presented in the appendix.

AB - Let E be a rational elliptic curve and let K be an imaginary quadratic field. In this article we give a method to construct Heegner points when E has a prime bigger than 3 of additive reduction ramifying in the field K. The ideas apply to more general contexts, like constructing Darmon points attached to real quadratic fields, which is presented in the appendix.

KW - Heegner points

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EP - 926

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 2

ER -

On heegner points for primes of additive reduction ramifying in the base field

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Keywords

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