Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Failure of the local-global principle for isotropy of quadratic forms
  over function fields   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.

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The categories of this paper are: stat
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-ex
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con
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The categories of this paper are: cond-mat
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: patt-sol
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The categories of this paper are: eess
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The categories of this paper are: hep-ex