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Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations

 

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Opened Access Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations
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Author: Arias de Reyna Domínguez, Sara
Dieulefait, Luis Víctor
Wiese, Gabor
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2017-02
Published in: Transactions of the American Mathematical Society, 369 (2), 887-908.
Document type: Article
Abstract: This article is the first part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem. In this first part, we determine the smallest field over which the projectivisation of a given symplectic group representation satisfying some natural conditions can be defined. The answer only depends on inner twists. We apply this to the residual representations of a compatible system of symplectic Galois representations satisfying some mild hypothesis and obtain precise information on their projective images for almost all members of the system, under the assumption of huge residual images, by which we mean that a symplectic group of full dimension over the prime field is contained up to conjugation. Finally, we obtain an application to the inverse Galois problem.
Cite: Arias de Reyna Domínguez, S., Dieulefait, L.V. y Wiese, G. (2017). Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations. Transactions of the American Mathematical Society 369 (2), 887-908
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URI: http://hdl.handle.net/11441/47639

DOI: 10.1090/tran/6708

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