Compositio Mathematica

Research Article

Functoriality and the inverse Galois problem

Chandrashekhar Kharea1a2, Michael Larsena3 and Gordan Savina1

a1 Department of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, USA (email:

a2 Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA (email:

a3 Department of Mathematics, Indiana University, Bloomington, IN 47405, USA (email:


We prove that, for any prime and any even integer n, there are infinitely many exponents k for which $\mathrm {PSp}_n(\mathbb {F}_{\ell ^k})$ appears as a Galois group over $\mathbb {Q}$. This generalizes a result of Wiese from 2006, which inspired this paper.

(Received December 12 2006)

(Accepted September 03 2007)

(Online publication March 14 2008)


  • automorphic forms;
  • Galois representations

2000 Mathematics subject classification

  • 11F;
  • 11R


CK was partially supported by NSF grants DMS 0355528 and DMS 0653821, and the Miller Institute for Basic Research in Science, University of California Berkeley. GS was partially supported by NSF grant DMS 0551846. ML was partially supported by NSF grant DMS 0354772.