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

Asher Auel and V. Suresh

Vol. 18 (2024), No. 8, 1497–1513
Abstract

We prove the failure of the local-global principle, with respect to discrete valuations, for isotropy of quadratic forms in 2n variables over function fields of transcendence degree n 2 over an algebraically closed field of characteristic 2. Our construction involves the generalized Kummer varieties considered by Borcea and by Cynk and Hulek as well as new results on the nontriviality of unramified cohomology of products of elliptic curves over discretely valued fields.

Keywords
quadratic forms, local-global principle, Hasse principle, function fields, unramified cohomology, elliptic curves
Mathematical Subject Classification
Primary: 11E04, 11R58, 12G05, 14G12
Secondary: 14H52, 14J32, 14J40, 19D45
Milestones
Received: 9 August 2022
Revised: 16 August 2023
Accepted: 18 September 2023
Published: 18 September 2024
Authors
Asher Auel
Department of Mathematics
Dartmouth College
Hanover, NH
United States
V. Suresh
Department of Mathematics
Emory University
Atlanta, GA
United States

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