Wild cyclic-by-tame extensions

Abstract

Suppose G is a semi-direct product of the form Z/p^n \rtimes Z/m where p is prime and m is relatively prime to p. Suppose K is a local field of characteristic p > 0. The main result states necessary and sufficient conditions on the ramification filtrations that occur for wildly ramified G-Galois extensions of K. In addition, we prove that there exists a parameter space for G-Galois extensions of K with given ramification filtration whose dimension depends only on the ramification filtration. We provide explicit equations for wild cyclic extensions of K of degree p^3.

15 pages, section 6.2 eliminated, major simplifications in former Proposition 4.3 (now Proposition 4.2), corrections in former Proposition 4.4 (now Proposition 4.3), many small changes in notations and language

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