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.
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The first author was supported in part by NSF Grant DMS-0500118.
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Harbater, D., Hartmann, J. & Krashen, D. Applications of patching to quadratic forms and central simple algebras. Invent. math. 178, 231–263 (2009). https://doi.org/10.1007/s00222-009-0195-5
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DOI: https://doi.org/10.1007/s00222-009-0195-5