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