Local-global principle for classical groups over function fields of \(p\)-adic curves (Q2159485)

Summary: Let \(K\) be a local field with residue field \(\kappa\) and \(F\) the function field of a curve over \(K\). Let \(G\) be a connected linear algebraic group over \(F\) of classical type. Suppose \(\operatorname{char} (\kappa)\) is a good prime for \(G\). Then we prove that projective homogeneous spaces under \(G\) over \(F\) satisfy a local-global principle for rational points with respect to discrete valuations of \(F\). If \(G\) is a semisimple simply connected group over \(F\), then we also prove that principal homogeneous spaces under \(G\) over \(F\) satisfy a local-global principle for rational points with respect to discrete valuations of \(F\).