Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The polylog quotient and the Goncharov quotient in computational
  Chabauty-Kim theory I   Polylogarithms are those multiple polylogarithms that factor through a
certain quotient of the de Rham fundamental group of the thrice punctured line
known as the polylogarithmic quotient. Building on work of Dan-Cohen, Wewers,
and Brown, we push the computational boundary of our explicit motivic version
of Kim's method in the case of the thrice punctured line over an open subscheme
of $\mathrm{Spec}\,\mathbb{Z}$. To do so, we develop a greatly refined version
of the algorithm of Dan-Cohen tailored specifically to this case, and we focus
attention on the polylogarithmic quotient. This allows us to restrict our
calculus with motivic iterated integrals to the so-called depth-one part of the
mixed Tate Galois group studied extensively by Goncharov. We also discover an
interesting consequence of the symmetry-breaking nature of the polylog quotient
that forces us to symmetrize our polylogarithmic version of Kim's conjecture.
  In this first part of a two-part series, we focus on a specific example,
which allows us to verify an interesting new case of Kim's conjecture.

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The categories of this paper are: econ
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The categories of this paper are: hep-th
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The categories of this paper are: eess
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The categories of this paper are: physics
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The categories of this paper are: chem-ph
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: adap-org
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The categories of this paper are: cond-mat
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The categories of this paper are: ao-sci
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The categories of this paper are: funct-an
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The categories of this paper are: atom-ph
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The categories of this paper are: nlin
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The categories of this paper are: dg-ga
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The categories of this paper are: q-bio