Wild monodromy and automorphisms of curves
| dc.creator | Lehr, Claus | |
| dc.creator | Matignon, Michel | |
| dc.date | 2004-12-15 | |
| dc.date | 2006-05-11 | |
| dc.date.accessioned | 2026-07-07T06:39:10Z | |
| dc.date.available | 2026-07-07T06:39:10Z | |
| dc.description | 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. | |
| dc.description | The final version of this article will be published in the Duke Mathematical Journal, published by Duke University press | |
| dc.identifier | https://arxiv.org/abs/math/0412294 | |
| dc.identifier | http://arxiv.org/abs/math/0412294 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/100981 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | Number Theory | |
| dc.subject | 11G20; 14H37; 14Q05 | |
| dc.title | Wild monodromy and automorphisms of curves | |
| dc.type | text |