Abstract
We study a ramification theory for a division algebra D of the following type: The center of D is a complete discrete valuation field K with the imperfect residue field F of certain type, and the residue algebra of D is commutative and purely inseparable over F. Using Swan conductors of the corresponding element of Br(K), we define Herbrand's ψ-function of D/K, and it describes the action of the reduced norm map on the filtration of D*. We also gives a relation among the Swan conductors and the 'ramification number' of D, which is defined by the commutator group of D*.
Original language | English |
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Pages (from-to) | 127-145 |
Number of pages | 19 |
Journal | Compositio Mathematica |
Volume | 112 |
Issue number | 2 |
DOIs | |
Publication status | Published - 1998 |
Externally published | Yes |
Keywords
- Brauer group
- Division algebra
- Reduced norm
- Swan conductor
- Wild ramification
ASJC Scopus subject areas
- Algebra and Number Theory