The index of the corestriction of a valued division algebra

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Abstract

Let L/F be a finite separable extension of Henselian valued fields with same residue fields L̄ = F̄. Let D be an inertially split division algebra over L, and let C D be the underlying division algebra of the corestriction corL/F (D) of D. We show that the index ind( C D) of C D divides [Z(D̄) : Z(C D)̄] · ind(D), where Z(D̄) is the center of the residue division ring D̄.

Original languageEnglish
Pages (from-to)279-284
Number of pages6
JournalJournal of the Korean Mathematical Society
Volume34
Issue number2
Publication statusPublished - 1997 Dec 1

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Keywords

  • Corestriction
  • Division Algebras
  • Henselian valuation

ASJC Scopus subject areas

  • Mathematics(all)

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