On the Integrality of Some Galois Representations

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1995Publisher:JSTORJournal:Proceedings of the American Mathematical Society, volume 123, page 299 (issn: 0002-9939,

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Authors: Gross, Robert;

doi: 10.2307/2160640 , 10.1090/s0002-9939-1995-1215201-0

On the Integrality of Some Galois Representations

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Abstract

We find an appropriate topology to put on K , the fraction field of the Iwasawa algebra Λ = Z p [ [ T ] ] \Lambda = {{\mathbf {Z}}_p}[[T]] , so that compact subgroups of K × {K^ \times } are in fact contained in Λ × {\Lambda ^ \times } . This ensures that Galois representations to K × {K^ \times } have image in Λ × {\Lambda ^ \times } .

Keywords

Iwasawa algebra, Galois theory, continuous Galois representations, Compact groups, compact subgroups

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