dc.creatorDembélé, Lassina
dc.creatorLoeffler, David
dc.creatorPacetti, Ariel Martín
dc.date.accessioned2020-12-03T19:17:49Z
dc.date.accessioned2022-10-14T21:31:07Z
dc.date.available2020-12-03T19:17:49Z
dc.date.available2022-10-14T21:31:07Z
dc.date.created2020-12-03T19:17:49Z
dc.date.issued2019-06-01
dc.identifierDembélé, Lassina; Loeffler, David; Pacetti, Ariel Martín; Non-paritious Hilbert modular forms; Springer; Mathematische Zeitschrift; 292; 1-2; 1-6-2019; 361-385
dc.identifier0025-5874
dc.identifierhttp://hdl.handle.net/11336/119772
dc.identifier1432-1823
dc.identifierCONICET Digital
dc.identifierCONICET
dc.identifier.urihttps://repositorioslatinoamericanos.uchile.cl/handle/2250/4308948
dc.description.abstractThe arithmetic of Hilbert modular forms has been extensively studied under the assumption that the forms concerned are “paritious”—all the components of the weight are congruent modulo 2. In contrast, non-paritious Hilbert modular forms have been relatively little studied, both from a theoretical and a computational standpoint. In this article, we aim to redress the balance somewhat by studying the arithmetic of non-paritious Hilbert modular eigenforms. On the theoretical side, our starting point is a theorem of Patrikis, which associates projectiveℓ-adic Galois representations to these forms. We show that a general conjecture of Buzzard and Gee actually predicts that a strengthening of Patrikis’ result should hold, giving Galois representations into certain groups intermediate between GL2 and PGL 2 ; and we verify that the predicted Galois representations do indeed exist. On the computational side, we give an algorithm to compute non-paritious Hilbert modular forms using definite quaternion algebras. To our knowledge, this is the first time such a general method has been presented. We end the article with an example.
dc.languageeng
dc.publisherSpringer
dc.relationinfo:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00209-019-02229-5
dc.relationinfo:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00209-019-02229-5
dc.rightshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.rightsinfo:eu-repo/semantics/openAccess
dc.subjectGALOIS REPRESENTATIONS
dc.subjectHILBERT MODULAR FORMS
dc.titleNon-paritious Hilbert modular forms
dc.typeinfo:eu-repo/semantics/article
dc.typeinfo:ar-repo/semantics/artículo
dc.typeinfo:eu-repo/semantics/publishedVersion


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