Applications of patching to quadratic forms and central simple algebras
Rings and Algebras
2009-04-24 v2 Algebraic Geometry
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.
Cite
@article{arxiv.0809.4481,
title = {Applications of patching to quadratic forms and central simple algebras},
author = {David Harbater and Julia Hartmann and Daniel Krashen},
journal= {arXiv preprint arXiv:0809.4481},
year = {2009}
}
Comments
48 pages; connectivity now required in the definition of rational group; beginning of Section 4 reorganized; other minor changes