, Volume 178, Issue 2, pp 231-263
Date: 21 Apr 2009

Applications of patching to quadratic forms and central simple algebras

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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 (in Preprint arXiv:0708.3128, 2007) on the u-invariant of p-adic function fields, p≠2. The strategy relies on a local-global principle for homogeneous spaces for rational algebraic groups, combined with local computations.

The first author was supported in part by NSF Grant DMS-0500118.