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


Authors: Daniel Kohen and Ariel Pacetti; with an Appendix by Marc Masdeu
Journal: Trans. Amer. Math. Soc. 370 (2018), 911-926
MSC (2010): Primary 11G05; Secondary 11G40
DOI: https://doi.org/10.1090/tran/6990
Published electronically: June 13, 2017
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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.


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Additional Information

Daniel Kohen
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, 2160 Buenos Aires, Argentina
Email: dkohen@dm.uba.ar

Ariel Pacetti
Affiliation: Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, 2160 Buenos Aires, Argentina
Address at time of publication: Facultad de Matemática, Astronomía y Física, Universidad Nacional de Córdoba, Av. Medina Allende s/n, Ciudad Universitaria, CP:X5000HUA Córdoba, Argentina
Email: apacetti@famaf.unc.edu.ar

Marc Masdeu
Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
Email: m.masdeu@warwick.ac.uk

DOI: https://doi.org/10.1090/tran/6990
Keywords: Heegner points
Received by editor(s): February 1, 2016
Received by editor(s) in revised form: May 11, 2016
Published electronically: June 13, 2017
Additional Notes: 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
Article copyright: © Copyright 2017 American Mathematical Society

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