Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ramification of Wild Automorphisms of Laurent Series Fields   Let $K$ be a complete discrete valuation field with residue class field $k$,
where both are of positive characteristic $p$. Then the group of wild
automorphisms of $K$ can be identified with the group under composition of
formal power series over $k$ with no constant term and $X$-coefficient $1$.
Under the hypothesis that $p > b^2$, we compute the first nontrivial
coefficient of the $p$th iterate of a power series over $k$ of the form $f = X
+ \sum_{i \geq 1} a_iX^{b+i}$. As a result, we obtain a necessary and
sufficient condition for an automorphism to be ``$b$-ramified,'' having lower
ramification numbers of the form $i_n(f) = b(1 + \cdots + p^n)$. This is a vast
generalization of Nordqvist's 2017 theorem on $2$-ramified power series, as
well as the analogous result for minimally ramified power series which proved
to be useful for arithmetic dynamics in a 2013 paper of Lindahl on
linearization discs in $\mathbf{C}_p$ and a 2015 result of
Lindahl--Rivera-Letelier on optimal cycles over nonarchimedean fields of
positive residue characteristic. The success of our computation is also
promising progress towards a generalization of Lindahl--Nordqvist's 2018
theorem bounding the norm of periodic points of $2$-ramified power series.

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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: physics
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The categories of this paper are: math-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: quant-ph
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The categories of this paper are: q-bio
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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: eess
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The categories of this paper are: q-fin