Reduced norm map of division algebras over complete discrete valuation fields of certain type

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3 Citations (Scopus)

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 languageEnglish
Pages (from-to)127-145
Number of pages19
JournalCompositio Mathematica
Volume112
Issue number2
DOIs
Publication statusPublished - 1998
Externally publishedYes

Keywords

  • Brauer group
  • Division algebra
  • Reduced norm
  • Swan conductor
  • Wild ramification

ASJC Scopus subject areas

  • Algebra and Number Theory

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