Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Etale Steenrod operations and the Artin-Tate pairing   We prove a 1966 conjecture of Tate concerning the Artin-Tate pairing on the
Brauer group of a surface over a finite field, which is the analogue of the
Cassels-Tate pairing. Tate asked if this pairing is always alternating and we
find an affirmative answer, which is somewhat surprising in view of the work of
Poonen-Stoll on the Cassels-Tate pairing. Our method is based on studying a
connection between the Artin-Tate pairing and (generalizations of) Steenrod
operations in \'{e}tale cohomology. Inspired by an analogy to the algebraic
topology of manifolds, we develop tools allowing us to calculate the relevant
\'{e}tale Steenrod operations in terms of characteristic classes.

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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: gr-qc
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The categories of this paper are: eess
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph
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The categories of this paper are: cs
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph