Abstract:
Let ρ1 and ρ2 be a pair of residual, odd, absolutely irreducible two-dimensional Galois representations of a totally real number field F. In this article we propose a conjecture asserting existence of “safe” chains of compatible systems of Galois representations linking ρ1 to ρ2. Such conjecture implies the generalized Serre’ conjecture and is equivalent to Serre’ conjecture under a modular version of it. We prove a weak version of the modular variant using the connectedness of certain Hecke algebras, and we comment on possible applications of these results to establish some cases of Langlands functoriality. © Cambridge University Press 2015.
Registro:
| Documento: |
Parte de libro
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| Título: | Connectedness of hecke algebras and the rayuela conjecture: A path to functoriality and modularity |
| Autor: | Dieulefait, L.; Pacetti, A. |
| Filiación: | Departament d’Àlgebra i Geometria, Facultat de Matemàtiques, Universitat de Barcelona, Gran Via de les Corts Catalanes, 585, Barcelona, 08007, Spain
Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires and IMAS, CONICET, Argentina
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| Año: | 2015
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| Página de inicio: | 193
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| Página de fin: | 216
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| DOI: |
http://dx.doi.org/10.1017/CBO9781316106877.013 |
| Título revista: | Arithmetic and Geometry
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| Título revista abreviado: | Arithmetic and Geometry
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_97813161_v_n_p193_Dieulefait |
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Citas:
---------- APA ----------
Dieulefait, L. & Pacetti, A.
(2015)
. Connectedness of hecke algebras and the rayuela conjecture: A path to functoriality and modularity. Arithmetic and Geometry, 193-216.
http://dx.doi.org/10.1017/CBO9781316106877.013---------- CHICAGO ----------
Dieulefait, L., Pacetti, A.
"Connectedness of hecke algebras and the rayuela conjecture: A path to functoriality and modularity"
. Arithmetic and Geometry
(2015) : 193-216.
http://dx.doi.org/10.1017/CBO9781316106877.013---------- MLA ----------
Dieulefait, L., Pacetti, A.
"Connectedness of hecke algebras and the rayuela conjecture: A path to functoriality and modularity"
. Arithmetic and Geometry, 2015, pp. 193-216.
http://dx.doi.org/10.1017/CBO9781316106877.013---------- VANCOUVER ----------
Dieulefait, L., Pacetti, A. Connectedness of hecke algebras and the rayuela conjecture: A path to functoriality and modularity. Arithmetic and Geometry. 2015:193-216.
http://dx.doi.org/10.1017/CBO9781316106877.013