Article
Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties
Author/s | Arias de Reyna Domínguez, Sara
Dieulefait, Luis Víctor Shin, Sug Woo Wiese, Gabor |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2015-04 |
Deposit Date | 2016-10-13 |
Published in |
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Abstract | This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result ... This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part proves the following new result for the inverse Galois problem for symplectic groups. For any even positive integer n and any positive integer d, PSpn(Fℓd ) or PGSpn(Fℓd ) occurs as a Galois group over the rational numbers for a positive density set of primes ℓ. The result is obtained by showing the existence of a regular, algebraic, self-dual, cuspidal automorphic representation of GLn(AQ) with local types chosen so as to obtain a compatible system of Galois representations to which the results from Part II of this series apply. |
Project ID. | info:eu-repo/grantAgreement/MINECO/MTM2012-33830
DMS-1162250 1489 |
Citation | Arias de Reyna Domínguez, S., Dieulefait, L.V., Shin, S.W. y Wiese, G. (2015). Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties. Mathematische Annalen, 361 (3), 909-925. |
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