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- W2951704004 abstract "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." @default.
- W2951704004 created "2019-06-27" @default.
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- W2951704004 date "2004-12-15" @default.
- W2951704004 modified "2023-09-25" @default.
- W2951704004 title "Wild monodromy and automorphisms of curves" @default.
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