Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hilbert's Tenth Problem for function fields over valued fields in
  characteristic zero   Let K be a field with a valuation satisfying the following conditions: both K
and the residue field k have characteristic zero; the value group is not
2-divisible; there exists a maximal subfield F in the valuation ring such that
Gal(\bar{F}/F) and Gal(\bar{k}/k) have the same 2-cohomological dimension and
this dimension is finite. Then Hilbert's Tenth Problem has a negative answer
for any function field of a variety over K. In particular, this result proves
undecidability for varieties over C((T)).

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The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
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The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
16
The categories of this paper are: stat
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The categories of this paper are: adap-org
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The categories of this paper are: comp-gas
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: chem-ph