Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Uniform bounds for the number of rational points on varieties over
  global fields   We extend the work of Salberger; Walsh; Castryck, Cluckers, Dittmann and
Nguyen; and Vermeulen to prove the uniform dimension growth conjecture of
Heath-Brown and Serre for varieties of degree at least $4$ over global fields.
As an intermediate step, we generalize the bounds of Bombieri and Pila to
curves over global fields and in doing so we improve the $B^{\varepsilon}$
factor by a $\log(B)$ factor.

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The categories of this paper are: funct-an
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg