G.W.Berhuy@soton.ac.uk, tignol@math.ucl.ac.be

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

Full text: dvi.gz 80 k, dvi 202 k, ps.gz 844 k, pdf.gz 353 k, pdf 387 k.

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