Submission: 2006, Sep 15
Elaborating on techniques of Bayer-Fluckiger and Parimala, we prove the following strong version of Serre's Conjecture II for classical groups: let G be a simply connected absolutely simple group of outer type A_n or of type B_n, C_n or D_n (non trialitarian) defined over an arbitrary field F. If the separable dimension of F is at most 2 for every torsion prime of G, then every G-torsor is trivial.
2000 Mathematics Subject Classification: 11E72
Keywords and Phrases: hermitian form, generalized quadratic form, algebra with involution, quadratic pair
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