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dc.contributor.authorDarmon, Henri
dc.contributor.authorRotger Cerdà, Víctor
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtiques
dc.date.accessioned2018-02-06T13:49:38Z
dc.date.available2019-04-02T00:30:41Z
dc.date.issued2017-07-01
dc.identifier.citationDarmon, 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.issn0894-0347
dc.identifier.urihttp://hdl.handle.net/2117/113813
dc.description.abstractThis 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.extent72 p.
dc.language.isoeng
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi matemàtica::Equacions funcionals
dc.subject.lcshDifferential equations, Elliptic
dc.subject.otherElliptic curves
dc.subject.otherArtin representations
dc.subject.otherequivariant Birch and Swinnerton-Dyer conjecture
dc.subject.otherGross-Kudla-Schoen diagonal cycles
dc.subject.otherp-adic families of modular forms
dc.subject.otherEuler Systems
dc.titleDiagonal cycles and Euler systems II: the Birch and Swinnerton-Dyer conjecture for Hasse-Weil-Artin L-functions
dc.typeArticle
dc.subject.lemacEquacions diferencials el·líptiques
dc.contributor.groupUniversitat Politècnica de Catalunya. TN - Grup de Recerca en Teoria de Nombres
dc.identifier.doi10.1090/jams/861
dc.description.peerreviewedPeer Reviewed
dc.subject.amsClassificació AMS::35 Partial differential equations::35H Close-to-elliptic equations
dc.relation.publisherversionhttp://www.ams.org/journals/jams/2017-30-03/S0894-0347-2016-00861-5/
dc.rights.accessOpen Access
local.identifier.drac20335199
dc.description.versionPostprint (author's final draft)
local.citation.authorDarmon, H.; Rotger, V.
local.citation.publicationNameJournal of the American Mathematical Society
local.citation.volume30
local.citation.number3
local.citation.startingPage601
local.citation.endingPage672


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