Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Subfields of ample fields I. Rational maps and definability   Pop proved that a smooth curve C over an ample field K that has a K-rational
point has |K| many K-rational points. We strengthen this result by showing that
there are |K| many K-rational points that do not lie in a given proper
subfield, even after applying a rational map. As a consequence we gain insight
into the structure of existentially definable subsets of ample fields. In
particular, we prove that a perfect ample field has no existentially definable
proper infinite subfields.

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The categories of this paper are: bayes-an
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: funct-an
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The categories of this paper are: adap-org
1
The categories of this paper are: cs
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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: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex