Vanishing Cycles and Wild Monodromy

Details Vanishing Cycles and Wild Monodromy Vanishing Cycles and Wild Monodromy

2009-10-05

arxiv.org/abs/0910.0676v3

Mathematics

Algebraic Geometry

Appendix added, Section 5 reorganized (in particular, Example 5.12 added), other (smaller) changes, now 29 pages

Scientific paper

Let K be a complete discrete valuation field of mixed characteristic (0,p) with algebraically closed residue field, and let f: Y --> P^1 be a three-point G-cover defined over K, where G has a cyclic p-Sylow subgroup P. We examine the stable model of f, in particular, the minimal extension K^{st}/K such that the stable model is defined over K^{st}. Our main result is that, if g(Y) \geq 2, the ramification indices of f are prime to p, and |P| = p^n, then the p-Sylow subgroup of Gal(K^{st}/K) has exponent dividing p^{n-1}. This extends work of Raynaud in the case that |P| = p.

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