On Heegner points for primes of additive reduction ramifying in the base field
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- by Daniel Kohen and Ariel Pacetti; with an Appendix by Marc Masdeu PDF
- Trans. Amer. Math. Soc. 370 (2018), 911-926 Request permission
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.References
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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
- MR Author ID: 1157618
- 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
- MR Author ID: 759256
- Email: apacetti@famaf.unc.edu.ar
- Marc Masdeu
- Affiliation: Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom
- MR Author ID: 772165
- Email: m.masdeu@warwick.ac.uk
- 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 - © Copyright 2017 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 370 (2018), 911-926
- MSC (2010): Primary 11G05; Secondary 11G40
- DOI: https://doi.org/10.1090/tran/6990
- MathSciNet review: 3729491