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Ramification in the field of moduli. (Ramification dans les corps des modules.) (French) Zbl 1066.14016

Let \(f\) be an algebraic cover of the projective line, defined over \(\overline{\mathbb Q}\), with monodromy group \(G\) and let \(K\) be the compositum of residue fields of branch points of \(f\) and \(M\) the corresponding field of moduli. A result of S. Beckmann [J. Algebra 125, 236–255 (1989; Zbl 0698.14024)] gives information on the ramifications of bad places of \(f\) that divide the order of \(G\).
In this paper, the author studies the ramification of bad places of \(f\) that do not divide the order of \(G\), but for which the branch points of \(f\) meet when reduced. This is done by studying geometric and arithmetic aspects of completions of Hurwitz spaces.

MSC:

14E22 Ramification problems in algebraic geometry
14H30 Coverings of curves, fundamental group
12F12 Inverse Galois theory

Citations:

Zbl 0698.14024
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References:

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