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manuscripta mathematica

, Volume 93, Issue 1, pp 247–266 | Cite as

Galois cohomology of special orthogonal groups

  • Ryan Garibaldi
  • Jean-Pierre Tignol
  • Adrian R. Wadsworth
Article

Abstract

If (A,σ) is a central simple algebra of even degree with orthogonal involution, then for the map of Galois cohomology sets fromH 1(F,SO(A,σ)) to the 2-torsion in the Brauer group ofF, we describe fully the image of a given element ofH 1(F,SO(A,σ)) and prove that this description is correct in two different ways. As an easy consequence, we derive a result of Bartels [Bar, Satz 3].

Subject Classifications

12G05 20G15 16K20 11E88 

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Copyright information

© Springer-Verlag 1997

Authors and Affiliations

  • Ryan Garibaldi
    • 1
  • Jean-Pierre Tignol
    • 2
  • Adrian R. Wadsworth
    • 1
  1. 1.Dept. of MathematicsUniversity of California, San DiegoLa JollaUSA
  2. 2.Institut de MathématiqueUniversité Catholique de LouvainLouvain-La-NeuveBelgium

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