Article (Scientific journals)
Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations
ARIAS DE REYNA DOMINGUEZ, Sara; Dieulefait, Luis; WIESE, Gabor
2017In Transactions of the American Mathematical Society, 369, p. 887-908
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Keywords :
Mathematics - Number Theory; 11F80; 20C25; 12F12
Abstract :
[en] 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.
Disciplines :
Mathematics
Author, co-author :
ARIAS DE REYNA DOMINGUEZ, Sara 
Dieulefait, Luis
WIESE, Gabor  ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Language :
English
Title :
Compatible systems of symplectic Galois representations and the inverse Galois problem I. Images of projective representations
Publication date :
2017
Journal title :
Transactions of the American Mathematical Society
ISSN :
1088-6850
Publisher :
American Mathematical Society
Volume :
369
Pages :
887-908
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBilu :
since 20 November 2013

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