Article
Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image
Author/s | Arias de Reyna Domínguez, Sara
Dieulefait, Luis Víctor Wiese, Gabor |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2016-03 |
Deposit Date | 2016-10-13 |
Published in |
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Abstract | This article is the second part of a series of three articles about compatible
systems of symplectic Galois representations and applications to the inverse
Galois problem. This part is concerned with symplectic Galois ... This article is the second part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. This part is concerned with symplectic Galois representations having a huge residual image, by which we mean that a symplectic group of full dimension over the prime field is contained up to conjugation. A key ingredient is a classification of symplectic representations whose image contains a nontrivial transvection: these fall into three very simply describable classes, the reducible ones, the induced ones and those with huge image. Using the idea of an (n,p)-group of Khare, Larsen and Savin, we give simple conditions under which a symplectic Galois representation with coefficients in a finite field has a huge image. Finally, we combine this classification result with the main result of the first part to obtain a strengthened application to the inverse Galois problem. |
Project ID. | info:eu-repo/grantAgreement/MINECO/MTM2012-33830
1489 INTER/DFG/12/10/COMFGREP |
Citation | Arias de Reyna Domínguez, S., Dieulefait, L.V. y Wiese, G. (2016). Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image. Pacific Journal of Mathematics, 281 (1), 1-16. |
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