Functoriality and the Inverse Galois problem II: groups of type B_n and G_2

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dc.creatorKhare, Chandrashekhar
dc.creatorLarsen, Michael
dc.creatorSavin, Gordan
dc.date2008-07-05
dc.date.accessioned2026-07-07T09:48:42Z
dc.date.available2026-07-07T09:48:42Z
dc.descriptionFor every finite field F and every positive integer r, there exists a finite extension F' of F such that either SO(2r+1,F') or its simple derived group can be realized as a Galois group over Q. If the characteristic of F is 3 or 5 (mod 8), then we can guarantee that the derived group of SO(2r+1,F') can be realized. Likewise, for every finite field F, there exists a finite extension F' of F such that the finite simple group G_2(F') can be realized a Galois group over Q. The proof uses automorphic forms to construct Galois representations which cut out Galois extensions of the desired type.
dc.description25 pages
dc.identifierhttps://arxiv.org/abs/0807.0861
dc.identifierhttp://arxiv.org/abs/0807.0861
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/164312
dc.subjectNumber Theory
dc.subject11F70; 11F80; 12F12
dc.titleFunctoriality and the Inverse Galois problem II: groups of type B_n and G_2
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