Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Distribution Relation and Inverse Function Theorem in Arithmetic
  Geometry   We study arithmetic distribution relations and the inverse function theorem
in algebraic and arithmetic geometry, with an emphasis on versions that can be
applied uniformly across families of varieties and maps. In particular, we
prove two explicit versions of the inverse function theorem, the first via
general distribution and separation inequalities that may be of independent
interest, the second via a careful implementation of classical Newton
iteration.

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The categories of this paper are: nlin
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The categories of this paper are: supr-con
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: cond-mat
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: hep-lat