Correspondences between valued division algebras and graded division algebras

Yoon Sung Hwang, A. R. Wadsworth

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34 Citations (Scopus)

Abstract

If D is a tame central division algebra over a Henselian valued field F, then the valuation on D yields an associated graded ring GD which is a graded division ring and is also central and graded simple over GF. After proving some properties of graded central simple algebras over a graded field (including a cohomological characterization of its graded Brauer group), it is proved that the map [D] → [GD]g yields an index-preserving isomorphism from the tame part of the Brauer group of F to the graded Brauer group of GF. This isomorphism is shown to be functorial with respect to field extensions and corestrictions, and using this it is shown that there is a correspondence between F-subalgebras of D (with center tame over F) and graded GF-subalgebras of GD.

Original languageEnglish
Pages (from-to)73-114
Number of pages42
JournalJournal of Algebra
Volume220
Issue number1
Publication statusPublished - 1999 Oct 1

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ASJC Scopus subject areas

  • Algebra and Number Theory

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