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Nonsolvable number fields ramified only at 3 and 5

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Dembélé, Lassina, Greenberg, Matthew and Voight, John. (2011) Nonsolvable number fields ramified only at 3 and 5. Compositio Mathematica, Vol.147 (No.3). pp. 716-734. ISSN 0010-437X

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Official URL: http://dx.doi.org/10.1112/S0010437X10005105

Abstract

For p = 3 and p = 5, we exhibit a finite nonsolvable extension of Q which is ramified only at p, proving in the affirmative a conjecture of Gross. Our construction involves explicit computations with Hilbert modular forms.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH):	Hilbert modular surfaces, Galois theory
Journal or Publication Title:	Compositio Mathematica
Publisher:	Cambridge University Press
ISSN:	0010-437X
Date:	May 2011
Volume:	Vol.147
Number:	No.3
Page Range:	pp. 716-734
Identification Number:	10.1112/S0010437X10005105
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Deutsche Forschungsgemeinschaft (DFG), Natural Sciences and Engineering Research Council of Canada (NSERC), National Science Foundation (U.S.) (NSF)
Grant number:	SFB/TR 45 (DFG), DMS-0901971 (NSF)
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URI:	http://wrap.warwick.ac.uk/id/eprint/39991