Applications of patching to quadratic forms and central simple algebras
By D. Harbater, Julia Hartmann, Daniel Krashen. 2008
133 citations recorded by the source corpus.
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.
Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/c7115572d26ada8e69e913839d3586de60a9f311
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In Computational Theory and Mathematics
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Citations in the corpus
- Open problems on central simple algebras (2010, background): “Sal97a], [Sal07], [Bru10], [PS98], [PSar]; De Jong’s result on the Brauer group of the function field of a complex surface, see [dJ04], [Lie08], and §4; Harbater–Hartmann–Krashenpatchingtechniques, see[HHK09]and [HHKar]; and Merkurjev’sboundingofessentialp-dimensionof PGLn, see[Mer10], [Merar], and §”
- Patching and local-global principles for homogeneous spaces over function fields of p-adic curves (2008, background): “We say that a field F is a C0r field if the following condition holds : For any finite field extension F ′ of F and any integers d ≥ 1 and n > dr, for any homogeneous form over F ′ of degree d in n variables, the g.c.d. of the degrees of finite field extensions F ′′/F ′ over which the form acquires…”