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Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions
dc.contributor.author | Darmon, Henri |
dc.contributor.author | Rotger Cerdà, Víctor |
dc.contributor.other | Universitat Politècnica de Catalunya. Departament de Matemàtiques |
dc.date.accessioned | 2018-02-06T13:49:38Z |
dc.date.available | 2019-04-02T00:30:41Z |
dc.date.issued | 2017-07-01 |
dc.identifier.citation | 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. |
dc.identifier.issn | 0894-0347 |
dc.identifier.uri | http://hdl.handle.net/2117/113813 |
dc.description.abstract | 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. |
dc.format.extent | 72 p. |
dc.language.iso | eng |
dc.subject | Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Equacions funcionals |
dc.subject.lcsh | Differential equations, Elliptic |
dc.subject.other | Elliptic curves |
dc.subject.other | Artin representations |
dc.subject.other | equivariant Birch and Swinnerton-Dyer conjecture |
dc.subject.other | Gross-Kudla-Schoen diagonal cycles |
dc.subject.other | p-adic families of modular forms |
dc.subject.other | Euler Systems |
dc.title | Diagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions |
dc.type | Article |
dc.subject.lemac | Equacions diferencials el·líptiques |
dc.contributor.group | Universitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres |
dc.identifier.doi | 10.1090/jams/861 |
dc.description.peerreviewed | Peer Reviewed |
dc.subject.ams | Classificació AMS::35 Partial differential equations::35H Close-to-elliptic equations |
dc.relation.publisherversion | http://www.ams.org/journals/jams/2017-30-03/S0894-0347-2016-00861-5/ |
dc.rights.access | Open Access |
local.identifier.drac | 20335199 |
dc.description.version | Postprint (author's final draft) |
local.citation.author | Darmon, H.; Rotger, V. |
local.citation.publicationName | Journal of the American Mathematical Society |
local.citation.volume | 30 |
local.citation.number | 3 |
local.citation.startingPage | 601 |
local.citation.endingPage | 672 |
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