✦ LIBER ✦
Generalized Cocycles with Values in One-Units of Henselian Valued Division Algebras
✍ Scribed by Patrick J. Morandi; B.A. Sethuraman
- Publisher
- Elsevier Science
- Year
- 2000
- Tongue
- English
- Weight
- 155 KB
- Volume
- 224
- Category
- Article
- ISSN
- 0021-8693
No coin nor oath required. For personal study only.
✦ Synopsis
Let ZrF be an inertial Galois extension of Henselian valued fields, and let D be a Z-central division algebra. Let G be a finite group acting on Z with fixed field F. We show that every generalized cocycle of G with values in the one-units Ž . of D is cohomologous to one of the form , 1 , or in other words, the existence of such a cocycle implies that the group action of G on Z extends to a group action on D. We provide applications to lifting of group actions on the residue division algebra and to the existence of Kummer subfields in D given suitable data in D.