Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An explicit theory of $\pi_{1}^\mathrm{un,crys}(\mathbb{P}^{1} -
  \{0,\mu_{N},\infty\})$ - II-3 : Sequences of multiple harmonic sums viewed as
  periods   Let $X=\text{ }\mathbb{P}^{1} - (\{0,\infty\} \cup \mu_{N})\text{ }/\text{
}W(\mathbb{F}_{q})$, with $N \in \mathbb{N}^{\ast}$ and $\mathbb{F}_{q}$ of
characteristic $p$ prime to $N$ and containing a primitive $N$-th root of
unity. We establish an explicit theory of the crystalline Frobenius of the
pro-unipotent fundamental groupoid of $X$. In part I, we have computed
explicitly the Frobenius action. In part II, we use this computation to
understand explicitly the algebraic relations of cyclotomic $p$-adic multiple
zeta values. We have used the ideas and the vocabulary of the Galois theory of
periods, and in our framework, certain sequences of prime weighted multiple
harmonic sums have been dealt with as if they were periods. In this II-3, we
define three notions which essentialize our three types of computations,
respectively : a "continuous" groupoid
$\pi_{1}^{\un,\DR}(X_{K})^{\hat{\text{cont}}}$, a "localization"
$\pi_{1}^{\un,\DR}(X_{K})^{\loc}$ of $\pi_{1}^{\un,\DR}(X_{K})$, and a
"rational counterpart at zero" $\pi_{1}^{\un,\RT,0}(X_{K})$ of
$\pi_{1}^{\un,\DR}(X_{K})$. As an application, and as a conlcusion of this part
II, we justify and clarify our Galois-theoretic point of view, in particular,
we construct period maps and state period conjectures for sequences of prime
weighted multiple harmonic sums.

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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-th
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th