2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/228134This paper provides applications of patching to quadratic forms and central simple algebras over function fields of curves over henselian valued fields. In particular, we use a patching approach to reprove and generalize a recent result of Parimala and Suresh on the u-invariant of p-adic function fields, for p odd. The strategy relies on a local-global principle for homogeneous spaces for rational algebraic groups, combined with local computations.48 pages; connectivity now required in the definition of rational group; beginning of Section 4 reorganized; other minor changesRings and AlgebrasAlgebraic Geometry11E04; 16K50; 14H05text