Applications of patching to quadratic forms and central simple algebras

Abstract

This 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 changes

Cited by in corpus (1)

• Patching subfields of division algebras