Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Wild monodromy and automorphisms of curves   Let $R$ be a complete discrete valuation ring of mixed characteristic $(0,p)$
with field of fractions $K$ containing the $p$-th roots of unity. This paper is
concerned with semi-stable models of $p$-cyclic covers of the projective line
$C \la \PK$. We start by providing a new construction of a semi-stable model of
$C$ in the case of an equidistant branch locus. If the cover is given by the
Kummer equation $Z^p=f(X_0)$ we define what we called the monodromy polynomial
${\mathcal L}(Y)$ of $f(X_0)$; a polynomial with coefficients in $K$. Its zeros
are key to obtaining a semi-stable model of $C$. As a corollary we obtain an
upper bound for the minimal extension $K'/K$ over which a stable model of the
curve $C$ exists. Consider the polynomial ${\cal L}(Y)\prod(Y^p-f(y_i))$ where
the $y_i$ range over the zeros of ${\cal L}(Y)$. We show that the splitting
field of this polynomial always contains $K'$, and that in some instances the
two fields are equal.

18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin
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The categories of this paper are: supr-con