Wild tame-by-cyclic extensions. (English) Zbl 1233.11125
Let \(K\) be a local field of characteristic \(p\) with algebraically closed residue field \(k\). Let \(G=C_{p^n}\rtimes C_m\) be a semidirect product of a cyclic group of order \(p^n\) with a cyclic group of order \(m\), where \(p\) is a prime number which doesn’t divide \(m\). A \(G\)-Galois extension of \(K\) is a Galois extension \(L/K\) together with an isomorphism of \(G\) with Gal\((L/K)\). In this paper the authors give necessary and sufficient conditions for a sequence of \(n\) rational numbers to be the positive upper ramification breaks of some \(G\)-Galois extension of \(K\). They also prove the existence of a coarse moduli space for isomorphism classes of \(G\)-Galois extensions of \(K\) with specified ramification data, and compute the \(k\)-dimension of this space.
Reviewer: Kevin Keating (Gainesville)
MSC:
| 11S15 | Ramification and extension theory |
| 11S20 | Galois theory |
| 14H30 | Coverings of curves, fundamental group |
| 14H10 | Families, moduli of curves (algebraic) |
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