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A non-solvable extension of ℚ unramified outside 7

Published online by Cambridge University Press:  24 January 2012

Luis V. Dieulefait*
Affiliation:
Departament d’Álgebra i Geometria, Universitat de Barcelona, Gran Via de les Corts Catalanes 585, 08007 Barcelona, Spain (email: [email protected])
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Abstract

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We consider a mod 7 Galois representation attached to a genus 2 Siegel cusp form of level 1 and weight 28 and using some of its Fourier coefficients and eigenvalues computed by N. Skoruppa and the classification of maximal subgroups of PGSp(4,p) we show that its image is as large as possible. This gives a realization of PGSp(4,7) as a Galois group over ℚ and the corresponding number field provides a non-solvable extension of ℚ which ramifies only at 7.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2012

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