Duke Mathematical Journal
- Duke Math. J.
- Volume 135, Number 3 (2006), 569-586.
Wild monodromy and automorphisms of curves
Let be a complete discrete valuation ring (DVR) of mixed characteristic with field of fractions containing the th roots of unity. This article is concerned with semistable models of -cyclic covers of the projective line . We start by providing a new construction of a semistable model of in the case of an equidistant branch locus. If the cover is given by the Kummer equation , we define what we call the monodromy polynomial of , a polynomial with coefficients in . Its zeros are key to obtaining a semistable model of . As a corollary, we obtain an upper bound for the minimal extension , over which a stable model of the curve exists. Consider the polynomial , where the range over the zeros of . We show that the splitting field of this polynomial always contains and that, in some instances, the two fields are equal
Duke Math. J., Volume 135, Number 3 (2006), 569-586.
First available in Project Euclid: 10 November 2006
Permanent link to this document
Digital Object Identifier
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