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Alternating groups as monodromy groups in positive characteristic

Irene I. Bouw·Stefan Wewers
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Abstract

Let $X$ be a generic curve of genus $g$ defined over an algebraically closed field $k$ of characteristic $p\geq 0$. We show that for $n$ sufficiently large there exists a tame rational map $f:X\to \PP^1_k$ with monodromy group $A_n$. This generalizes a result of Magaard--Völklein to positive characteristic.

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Irene I. Bouw, Stefan Wewers. 2004-09-21. Alternating groups as monodromy groups in positive characteristic. https://arxiv.org/abs/math/0402436

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