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

Departament de Matemàtiques

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Resum

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.

Idioma original	Anglès
Pàgines (de-a)	911-926
Nombre de pàgines	16
Revista	Transactions of the American Mathematical Society
Volum	370
Número	2
DOIs	https://doi.org/10.1090/tran/6990
Estat de la publicació	Publicada - de febr. 2018

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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.",

year = "2018",

month = feb,

doi = "10.1090/tran/6990",

language = "English",

volume = "370",

pages = "911--926",

journal = "Transactions of the American Mathematical Society",

issn = "0002-9947",

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AU - Kohen, Daniel

AU - Pacetti, Ariel

AU - Masdeu, Marc

N1 - 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: © 2017 American Mathematical Society.

PY - 2018/2

Y1 - 2018/2

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

UR - https://www.scopus.com/pages/publications/85036577987

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DO - 10.1090/tran/6990

M3 - Article

AN - SCOPUS:85036577987

SN - 0002-9947

VL - 370

SP - 911

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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