English

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.

Keywords

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

R2 v1 2026-06-21T11:24:18.065Z