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arXiv · 1606.08592

Wild ramification of nilpotent coverings and coverings of bounded degree

Lars Kindler
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Abstract

A finite \'etale map between irreducible, normal varieties is called tame, if it is tamely ramified with respect to all partial compactifications whose boundary is the support of a strict normal crossings divisor. We prove that if the Galois group of a Galois covering contains a normal nilpotent subgroup of index bounded by a constant N, then the covering is tame if and only if it is tamely ramified with respect to a single distinguished partial compactification only depending on N. The main tools used in the proof are Temkin's local purely inseparable uniformization and a Lefschetz type theorem due to Drinfeld.

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Lars Kindler. 2016-06-28. Wild ramification of nilpotent coverings and coverings of bounded degree. https://arxiv.org/abs/1606.08592

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