Submission: 2004, Oct 5
Let K be a Henselian discrete valued field with real closed residue field k. Central simple algebras of exponent 2 over the rational function field K(x), which are trivial over all real closures of K(X) (so called Omega-algebras) are studied. It follows from a result of Becher that such algebras are quaternion algebras. For algebras with special ramification explicit quadratic splitting fields are constructed. The results also give some information over relatively minimal coninc bundles over the projective line over K.
2000 Mathematics Subject Classification: 12D15, 12E15, 16K05, 11E10, 12J25
Keywords and Phrases: Henselian discrete valued fields, Quaternion division algebras, Brauer group, u-invariant, conic bundles
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