Abstract
Let K be a complete discrete valued field with residue field k and F the function field of a curve over K. Let A∈2Br(F) be a central simple algebra with an involution σ of any kind and F0=Fσ. Let h be an hermitian space over (A,σ) and G=SU(A,σ,h) if σ is of first kind and G=U(A,σ,h) if σ is of second kind. Suppose that char(k)≠2 and ind(A)≤4. Then we prove that projective homogeneous spaces under G over F0 satisfy a local-global principle for rational points with respect to discrete valuations of F.
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