Compatible systems of symplectic Galois representations and the inverse Galois problem III. Automorphic construction of compatible systems with suitable local properties
Abstract
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, selfdual, 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.
 Publication:

arXiv eprints
 Pub Date:
 August 2013
 arXiv:
 arXiv:1308.2192
 Bibcode:
 2013arXiv1308.2192A
 Keywords:

 Mathematics  Number Theory;
 11F80;
 12F12
 EPrint:
 Minor modifications. 17 pages