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Functoriality and the inverse Galois problem

Published online by Cambridge University Press:  01 May 2008

Chandrashekhar Khare,
Michael Larsen and
Gordan Savin
Chandrashekhar Khare
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, USA (email: shekhar@math.utah.edu)Department of Mathematics, UCLA, Los Angeles, CA 90095-1555, USA (email: larsen@math.indiana.edu)
Michael Larsen
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA (email: savin@math.utah.edu)
Gordan Savin
Affiliation:
Department of Mathematics, University of Utah, 155 South 1400 East, Room 233, Salt Lake City, UT 84112-0090, USA (email: shekhar@math.utah.edu)
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Abstract

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We prove that, for any prime ℓ 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.

Keywords

automorphic formsGalois representations

Information

Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 3 , May 2008, pp. 541 - 564
Copyright
Copyright © Foundation Compositio Mathematica 2008

References

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.