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Title:
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Heegner points on Hijikata-Pizer-Shemanske curves and the Birch and Swinnerton-Dyer conjecture
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Author:
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Longo, Matteo; Rotger Cerdà, Víctor; Vera Piquero, Carlos de
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Other authors:
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Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
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Abstract:
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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. |
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Abstract:
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Peer Reviewed |
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Subject(s):
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-Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica
-Arithmetical algebraic geometry
-BSD conjecture
-Heegner points
-L-functions
-Shimura curves
-Geometria algèbrica--Aritmètica
-Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) |
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Rights:
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Document type:
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Article - Submitted version
Article |
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