科研之友
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摘要
Suppose G is a semi-direct product of the form Z/p(n) x Z/m where p is prime and in is relatively prime to p. Suppose K is a complete discrete valuation field of characteristic p > 0 with algebraically closed residue field. 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, and we calculate its dimension in terms of the ramification filtration. We provide explicit equations for wild cyclic extensions of K of degree p(3).
- 出版日期2010-5
