Applications of patching to quadratic forms and central simple algebras

Details Applications of patching to quadratic forms and central simple algebras Applications of patching to quadratic forms and central simple algebras

2008-09-25

arxiv.org/abs/0809.4481v2

Mathematics

Rings and Algebras

48 pages; connectivity now required in the definition of rational group; beginning of Section 4 reorganized; other minor chang

Scientific paper

10.1007/s00222-009-0195-5

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.

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