Reference : Compatible systems of symplectic Galois representations and the inverse Galois proble...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
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 mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Transactions of the American Mathematical Society
American Mathematical Society
Yes (verified by ORBilu)
[en] Mathematics - Number Theory ; 11F80 ; 20C25 ; 12F12
[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.

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