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

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hdl:2117/123220
Document typeArticle
Defense date2018-01-01
Rights accessOpen Access
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Abstract
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.
CitationLongo, Matteo, Rotger, V., de Vera, C. Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture. "Publicacions matemàtiques", 1 Gener 2018, vol. 62, núm. 2, p. 355-396.
ISSN0214-1493
Publisher versionhttp://mat.uab.cat/pubmat/articles/view_doi/10.5565/PUBLMAT6221803
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