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/10993/11495
Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties
English
Arias De Reyna Dominguez, Sara mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Dieulefait, L. [> >]
Shin, S. W. [> >]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
2015
Mathematische Annalen
Springer
361
3
909-925
Yes
International
[en] Mathematics - Number Theory ; 11F80 ; 12F12
[en] This article is the third and last part of a series of three articles about compatible systems of symplectic Galois representations and applications to the inverse Galois problem.
This part proves the following new result for the inverse Galois problem for symplectic groups. For any even positive integer n and any positive integer d, PSp_n(F_{l^d}) or PGSp_n(F_{l^d}) occurs as a Galois group over the rational numbers for a positive density set of primes l.
The result is obtained by showing the existence of a regular, algebraic, self-dual, cuspidal automorphic representation of GL_n(A_Q) with local types chosen so as to obtain a compatible system of Galois representations to which the results from Part II of this series apply.
Researchers
http://hdl.handle.net/10993/11495
10.1007/s00208-014-1091-x

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