Number Theory pp 165-195
Galois coverings of the arithmetic line
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- Harbater D. (1987) Galois coverings of the arithmetic line. In: Chudnovsky D.V., Chudnovsky G.V., Cohn H., Nathanson M.B. (eds) Number Theory. Lecture Notes in Mathematics, vol 1240. Springer, Berlin, Heidelberg
This paper concerns Galois branched coverings of the line, first over the complex numbers and then over the p-adics. We construct such covers with arbitrary Galois group, and then descend these to covers defined over number fields. In particular, every finite group is shown to occur as a Galois group over Open image in new window. This is a consequence of a more general result that also implies that complete local domains other than fields are never Hilbertian — thus answering a question of Lang.
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