Inventiones mathematicae

, Volume 178, Issue 2, pp 231–263

Applications of patching to quadratic forms and central simple algebras

Article

DOI: 10.1007/s00222-009-0195-5

Cite this article as:
Harbater, D., Hartmann, J. & Krashen, D. Invent. math. (2009) 178: 231. doi:10.1007/s00222-009-0195-5

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.

Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  • David Harbater
    • 1
  • Julia Hartmann
    • 2
  • Daniel Krashen
    • 3
  1. 1.Department of MathematicsUniversity of PennsylvaniaPhiladelphiaUSA
  2. 2.Lehrstuhl A für MathematikRWTH Aachen UniversityAachenGermany
  3. 3.Department of MathematicsUniversity of GeorgiaAthensUSA

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