Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture

Longo, Matteo ; Rotger, Víctor ; de Vera-Piquero, Carlos

Resumen: We study Heegner points on elliptic curves, or more generally modular abelian varieties, coming from uniformization by Shimura curves attached to a rather general type of quaternionic orders. We address several questions arising from the Birch and Swinnerton-Dyer (BSD) conjecture in this general context. In particular, under mild technical conditions, we show the existence of non-torsion Heegner points on elliptic curves in all situations in which the BSD conjecture predicts their existence.

Idioma: Inglés

DOI: 10.5565/PUBLMAT6221803

Año: 2018

Publicado en: Publicacions Matematiques 62 (2018), 355-396
ISSN: 0214-1493

Factor impacto JCR: 1.41 (2018)

Categ. JCR: MATHEMATICS rank: 44 / 313 = 0.141 (2018) - Q1 - T1

Factor impacto SCIMAGO: 0.875 - Mathematics (miscellaneous) (Q1)

Tipo y forma: Article (Published version)