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Explicit deformation of Galois representations

โœ Scribed by Nigel Boston


Book ID
105130273
Publisher
Springer-Verlag
Year
1991
Tongue
English
Weight
844 KB
Volume
103
Category
Article
ISSN
0020-9910

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โœ Sachiko Ohtani ๐Ÿ“‚ Article ๐Ÿ“… 2006 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 180 KB

We study the deformation theory of Galois representations whose restriction to every decomposition subgroup is abelian. As an application, we construct unramified non-solvable extensions over the field obtained by adjoining all p-power roots of unity to the field of rational numbers.

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In a previous paper the second author proved that the image of the Galois representation modulo attached to a Hilbert modular newform is "large" for all but finitely many primes , if the newform is not a theta series. In this brief note, we give an explicit bound for this exceptional finite set of p