Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finite field restriction estimates based on Kakeya maximal operator
  estimates   In the finite field setting, we show that the restriction conjecture
associated to any one of a large family of $d=2n+1$ dimensional quadratic
surfaces implies the $n+1$ dimensional Kakeya conjecture (Dvir's theorem). This
includes the case of the paraboloid over finite fields in which $-1$ \emph{is}
a square. We are able to partially reverse this implication using the sharp
Kakeya maximal operator estimates of Ellenberg, Oberlin and Tao to establish
the first finite field restriction estimates beyond the Stein-Tomas exponent in
this setting.

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The categories of this paper are: chao-dyn
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The categories of this paper are: bayes-an
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: plasm-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: math-ph
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The categories of this paper are: quant-ph