Reference : Compatible systems of symplectic Galois representations and the inverse Galois proble...
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/11504
Compatible systems of symplectic Galois representations and the inverse Galois problem II. Transvections and huge image
English
Arias De Reyna Dominguez, Sara mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Dieulefait, Luis [> >]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
2016
Pacific Journal of Mathematics
University of California
281
1
1-16
Yes (verified by ORBilu)
International
0030-8730
1945-5844
Berkeley
CA
[en] Mathematics - Number Theory ; 11F80 ; 20G14 ; 12F12
[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.
Researchers
http://hdl.handle.net/10993/11504
10.2140/pjm.2016.281.1

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
HI.pdfAuthor preprint314.03 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.