The u-invariant of the function fields of p-adic curves

By R. Parimala, V. Suresh. 2007

68 citations recorded by the source corpus.

The u-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the u-invariant of function fields of p-aidc curves is 8. In this paper, we answer this question in the affirmative for function fields of nondyadic p-adic curves.

Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/cfcfb48696df3b4c80e64cf4954b1c14d1f908d4

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In Algebra and Number Theory

In Applied Mathematics

In Geometry and Topology

Citations in the corpus

Patching and local-global principles for homogeneous spaces over function fields of p-adic curves (2008, methodology): “But they manage to apply the technique to the extent that they give a radically new proof of the theorem by Parimala and Suresh [ 27 ] that any quadratic form in at least 9 variables over K(X) (K as above, nondyadic, X a curve over K) has a nontrivial zero.”
Applications of patching to quadratic forms and central simple algebras (2008, methodology): “case, we obtain the recent theorem of Parimala and Suresh ([ PS07 ], Theorem 4.6; Corollary 4.15 below): A function field in one variable over a non-dyadic p-adic field has u-invariant 8. Our result also applies to function fields over the algebraic closure of Q in a non-dyadic p-adic field.”
Period-index and u-invariant questions for function fields over complete discretely valued fields (2013, background): “field K , this was proved in [28].”