Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hodge theory and the Mordell-Weil rank of elliptic curves over
  extensions of function fields   We use Hodge theory to prove a new upper bound on the ranks of Mordell-Weil
groups for elliptic curves over function fields after regular geometrically
Galois extensions of the base field, improving on previous results of Silverman
and Ellenberg, when the base field has characteristic zero and the supports of
the conductor of the elliptic curve and of the ramification divisor of the
extension are disjoint.

3
The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: hep-lat
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th