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Title:
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Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions
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Author:
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Darmon, Henri; Rotger Cerdà, Víctor
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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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This article establishes new cases of the Birch and Swinnerton-Dyer conjecture in analytic rank 0, for elliptic curves over $ \mathbb{Q}$ viewed over the fields cut out by certain self-dual Artin representations of dimension at most $ 4$. When the associated $ L$-function vanishes (to even order $ \ge 2$) at its central point, two canonical classes in the corresponding Selmer group are constructed and shown to be linearly independent assuming the non-vanishing of a Garrett-Hida $ p$-adic $ L$-function at a point lying outside its range of classical interpolation. The key tool for both results is the study of certain $ p$-adic families of global Galois cohomology classes arising from Gross-Kudla-Schoen diagonal cycles in a tower of triple products of modular curves. |
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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::Equacions funcionals
-Differential equations, Elliptic
-Elliptic curves
-Artin representations
-equivariant Birch and Swinnerton-Dyer conjecture
-Gross-Kudla-Schoen diagonal cycles
-p-adic families of modular forms
-Euler Systems
-Equacions diferencials el·líptiques
-Classificació AMS::35 Partial differential equations::35H Close-to-elliptic equations |
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Rights:
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Document type:
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Article - Submitted version
Article |
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