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Families of coverings of the projective line. (Familles de revêtements de la droite projective.) (French) Zbl 0888.11024
M. Fried introduced the concept of Hurwitz spaces in the inverse Galois theory. These spaces parametrize the isomorphism classes of coverings with certain data of ramification or of \(G\)-coverings of \(\mathbb{P}_1\). The first six chapters of the paper under review give a construction of the Hurwitz spaces, using classical algebraic topology. In §7 the author considers the algebraic situation and gives a new proof of a theorem of Fried-Völklein, which states that those Hurwitz spaces in question are over \(\mathbb{Q}\).

MSC:
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
12F12 Inverse Galois theory
11G35 Varieties over global fields
14D20 Algebraic moduli problems, moduli of vector bundles
14D22 Fine and coarse moduli spaces
14H10 Families, moduli of curves (algebraic)
14H30 Coverings of curves, fundamental group
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