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Reduced Norm Map of Division Algebras over Complete Discrete Valuation Fields of Certain Type
Published online by Cambridge University Press: 04 December 2007
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 ψ-function of D/K, and it describe 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$^*$.
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