Article (Scientific journals)
Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image
ARIAS DE REYNA DOMINGUEZ, Sara; Dieulefait, Luis; WIESE, Gabor
2016In Pacific Journal of Mathematics, 281 (1), p. 1-16
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Keywords :
Mathematics - Number Theory; 11F80; 20G14; 12F12
Abstract :
[en] 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. We prove a classification result on those subgroups of a general symplectic group over a finite field that contain a nontrivial transvection. Translating this group theoretic result into the language 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 strenghtened application to the inverse Galois problem.
Disciplines :
Mathematics
Author, co-author :
ARIAS DE REYNA DOMINGUEZ, Sara ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
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 II. Transvections and huge image
Publication date :
2016
Journal title :
Pacific Journal of Mathematics
ISSN :
0030-8730
eISSN :
1945-5844
Publisher :
University of California, Berkeley, United States - California
Volume :
281
Issue :
1
Pages :
1-16
Peer reviewed :
Peer Reviewed verified by ORBi
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