Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4597427 | Journal of Pure and Applied Algebra | 2010 | 9 Pages |
Abstract
Suppose G is a semi-direct product of the form Z/pnâZ/m where p is prime and m 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 p3.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Andrew Obus, Rachel Pries,