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.
|Number of pages||42|
|Journal||Journal of Algebra|
|Publication status||Published - 1999 Oct 1|
ASJC Scopus subject areas
- Algebra and Number Theory