Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Descent on elliptic surfaces and arithmetic bounds for the Mordell-Weil
  rank   We introduce the use of $p$-descent techniques for elliptic surfaces over a
perfect field of characteristic not $2$ or $3$. Under mild hypotheses, we
obtain an upper bound for the rank of a non-constant elliptic surface. When
$p=2$, this bound is an arithmetic refinement of a well-known geometric bound
for the rank deduced from Igusa's inequality. This answers a question raised by
Ulmer. We give some applications to rank bounds for elliptic surfaces over the
rational numbers.

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The categories of this paper are: q-bio
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The categories of this paper are: atom-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: q-fin
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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: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs
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The categories of this paper are: hep-lat
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The categories of this paper are: math-ph