Wild tame-by-cyclic extensions
Suppose G is a semi-direct product of the form Z / p n ⋊ Z / 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 rami...
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| Published in | Journal of pure and applied algebra Vol. 214; no. 5; pp. 565 - 573 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Elsevier B.V
01.05.2010
|
| Subjects | |
| Online Access | Get full text |
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| Summary: | Suppose
G
is a semi-direct product of the form
Z
/
p
n
⋊
Z
/
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
p
3
. |
|---|---|
| ISSN: | 0022-4049 1873-1376 |
| DOI: | 10.1016/j.jpaa.2009.06.017 |