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Correspondences Between Valued Division Algebras and Graded Division Algebras

โœ Scribed by Y.-S Hwang; A.R Wadsworth

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
327 KB
Volume
220
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

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 โ†’ 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.

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