Failure of the local-global principle for isotropy of quadratic forms over function fields

Abstract

We prove the failure of the local-global principle, with respect to discrete valuations, for isotropy of quadratic forms over function fields of transcendence degree at least 2 over algebraically closed fields. Our construction involves generalized Kummer varieties as well as a new nontriviality result for the unramified cohomology of products of elliptic curves over discretely valued fields, which can be viewed as an arithmetic version of a theorem of Gabber.

15 pages, final version accepted in Algebra & Number Theory

References in corpus (1)

• An exact sequence for Milnor's K-theory with applications to quadratic forms