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 language | English |
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Pages (from-to) | 73-114 |
Number of pages | 42 |
Journal | Journal of Algebra |
Volume | 220 |
Issue number | 1 |
DOIs | |
Publication status | Published - 1999 Oct 1 |
ASJC Scopus subject areas
- Algebra and Number Theory