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Tate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type

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dc.contributor.authorFité Naya, Francesc
dc.contributor.authorGuitart Morales, Xavier
dc.date.accessioned2023-02-13T17:24:39Z
dc.date.available2023-11-06T06:10:24Z
dc.date.issued2022-11-06
dc.date.updated2023-02-13T17:24:39Z
dc.description.abstractAbstract. We introduce a tensor decomposition of the $\ell$-adic Tate module of an abelian variety $A_0$ defined over a number field which is geometrically isotypic and potentially of $\mathrm{GL}_2$-type. We use this decomposition as a fundamental tool to describe the Sato-Tate group of $A_0$ and to prove the Sato-Tate conjecture in certain cases.
dc.format.extent21 p.
dc.format.mimetypeapplication/pdf
dc.identifier.idgrec717404
dc.identifier.issn0025-5874
dc.identifier.urihttps://hdl.handle.net/2445/193536
dc.language.isoeng
dc.publisherSpringer Verlag
dc.relation.isformatofVersió postprint del document publicat a: https://doi.org/10.1007/s00209-021-02895-4
dc.relation.ispartofMathematische Zeitschrift, 2022, vol. 300, num. 3, p. 2975-2995
dc.relation.urihttps://doi.org/10.1007/s00209-021-02895-4
dc.rights(c) Springer Verlag, 2022
dc.rights.accessRightsinfo:eu-repo/semantics/openAccess
dc.sourceArticles publicats en revistes (Matemàtiques i Informàtica)
dc.subject.classificationVarietats abelianes
dc.subject.classificationGrups discontinus
dc.subject.classificationGeometria algebraica
dc.subject.classificationTeoria de nombres
dc.subject.otherAbelian varieties
dc.subject.otherDiscontinuous groups
dc.subject.otherAlgebraic geometry
dc.subject.otherNumber theory
dc.titleTate module tensor decompositions and the Sato-Tate conjecture for certain abelian varieties potentially of $\mathrm{GL}_2$-type
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:eu-repo/semantics/acceptedVersion

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