Applications of patching to quadratic forms and central simple algebras

2008/09/30 by David Harbater, Julia Hartmann, Daniel Krashen · 2 citations
Computer Science · Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Polynomial and algebraic computation #math.AG #math.RA #msc:11E04 #msc:14H05 #msc:16K50

paper · pdf · doi:10.1007/s00222-009-0195-5

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

arxiv created 2009/03/13 · openalex publication_date 2009/04/20 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/02

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.

Citations

• The u-invariant of the function fields of p-adic curves
• Commutative Algebra

Cited by

• The Pythagoras number and the u-invariant of Laurent series fields in several variables
• Patching over Berkovich curves and quadratic forms