On an isotropy criterion for quadratic forms over function fields of curves over non-dyadic complete discrete valuation rings
Harbater, Hartmann and Krashen obtained in 2015 a criterion for the existence of rational points on projective (or principal) homogeneous varieties for rational connected algebraic groups defined over function fields of normal curves over a complete discrete valuation ring in terms of completions of local rings at special points. This was obtained by a reduction via Artin approximation to a related patching problem solved by the same authors in 2009. In the special case of projective quadrics, we...