Duke Mathematical Journal

Wild monodromy and automorphisms of curves

Claus Lehr and Michel Matignon

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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

Article information

Duke Math. J., Volume 135, Number 3 (2006), 569-586.

First available in Project Euclid: 10 November 2006

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14H30: Coverings, fundamental group [See also 14E20, 14F35]
Secondary: 11C20: Matrices, determinants [See also 15B36]


Lehr, Claus; Matignon, Michel. Wild monodromy and automorphisms of curves. Duke Math. J. 135 (2006), no. 3, 569--586. doi:10.1215/S0012-7094-06-13535-4. https://projecteuclid.org/euclid.dmj/1163170202

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