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Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions

Autor
Darmon, H.; Rotger, V.
Tipus d'activitat
Article en revista
Revista
Journal of the American Mathematical Society
Data de publicació
2017-07-01
Volum
30
Número
3
Pàgina inicial
601
Pàgina final
672
DOI
https://doi.org/10.1090/jams/861 Obrir en finestra nova
Repositori
http://hdl.handle.net/2117/113813 Obrir en finestra nova
URL
http://www.ams.org/journals/jams/2017-30-03/S0894-0347-2016-00861-5/ Obrir en finestra nova
Resum
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$-f...
Citació
Darmon, H., Rotger, V. Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions. "Journal of the American Mathematical Society", 1 Juliol 2017, vol. 30, núm. 3, p. 601-672.
Paraules clau
Artin representations, Elliptic curves, Euler Systems, Gross-Kudla-Schoen diagonal cycles, equivariant Birch and Swinnerton-Dyer conjecture, p-adic families of modular forms
Grup de recerca
TN - Grup de Recerca en Teoria de Nombres

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