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dc.contributor.author
Dembélé, Lassina
dc.contributor.author
Loeffler, David
dc.contributor.author
Pacetti, Ariel Martín
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dc.date.available
2020-12-03T19:17:49Z
dc.date.issued
2019-06-01
dc.identifier.citation
Dembélé, Lassina; Loeffler, David; Pacetti, Ariel Martín; Non-paritious Hilbert modular forms; Springer; Mathematische Zeitschrift; 292; 1-2; 1-6-2019; 361-385
dc.identifier.issn
0025-5874
dc.identifier.uri
http://hdl.handle.net/11336/119772
dc.description.abstract
The 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.format
application/pdf
dc.language.iso
eng
dc.publisher
Springer
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
GALOIS REPRESENTATIONS
dc.subject
HILBERT MODULAR FORMS
dc.subject.classification
Matemática Pura
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dc.subject.classification
Matemáticas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Non-paritious Hilbert modular forms
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2020-11-19T21:20:14Z
dc.identifier.eissn
1432-1823
dc.journal.volume
292
dc.journal.number
1-2
dc.journal.pagination
361-385
dc.journal.pais
Alemania
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dc.journal.ciudad
Berlin
dc.description.fil
Fil: Dembélé, Lassina. Institute Max Planck For Mathematics; Alemania
dc.description.fil
Fil: Loeffler, David. University of Warwick; Reino Unido
dc.description.fil
Fil: Pacetti, Ariel Martín. University of Warwick; Reino Unido. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Centro de Investigación y Estudios de Matemática. Universidad Nacional de Córdoba. Centro de Investigación y Estudios de Matemática; Argentina
dc.journal.title
Mathematische Zeitschrift
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1007/s00209-019-02229-5
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/https://link.springer.com/article/10.1007/s00209-019-02229-5
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