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1 December 2006 Wild monodromy and automorphisms of curves
Claus Lehr, Michel Matignon
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Duke Math. J. 135(3): 569-586 (1 December 2006). DOI: 10.1215/S0012-7094-06-13535-4


Let R be a complete discrete valuation ring (DVR) of mixed characteristic (0,p) with field of fractions K containing the pth roots of unity. This article is concerned with semistable models of p-cyclic covers of the projective line CPK1. We start by providing a new construction of a semistable model of C in the case of an equidistant branch locus. If the cover is given by the Kummer equation Zp=f(X0), we define what we call the monodromy polynomial L(Y) of f(X0), a polynomial with coefficients in K. Its zeros are key to obtaining a semistable 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 L(Y)Π(Ypf(yi)), where the yi range over the zeros of L(Y). We show that the splitting field of this polynomial always contains K and that, in some instances, the two fields are equal


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Claus Lehr. Michel Matignon. "Wild monodromy and automorphisms of curves." Duke Math. J. 135 (3) 569 - 586, 1 December 2006.


Published: 1 December 2006
First available in Project Euclid: 10 November 2006

zbMATH: 1116.14020
MathSciNet: MR2272976
Digital Object Identifier: 10.1215/S0012-7094-06-13535-4

Primary: 14H30
Secondary: 11C20

Rights: Copyright © 2006 Duke University Press


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Vol.135 • No. 3 • 1 December 2006
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