Conductors of wild extensions of local fields, especially in mixed characteristic (0,2)
Number Theory
2015-03-03 v3
Abstract
If K_0 is the fraction field of the Witt vectors over an algebraically closed field k of characteristic p, we calculate upper bounds on the conductor of higher ramification for (the Galois closure of) extensions K_0(zeta_{p^r}, sqrt[p^r]{a})/K_0, where a is in K_0(zeta_{p^r}). Here zeta_{p^r} is a primitive p^r-th root of unity. In certain cases, including when a is in K_0 and p=2, we calculate the conductor exactly. These calculations can be used to determine the discriminants of various extensions of Q obtained by adjoining roots of unity and radicals.
Keywords
Cite
@article{arxiv.1109.4776,
title = {Conductors of wild extensions of local fields, especially in mixed characteristic (0,2)},
author = {Andrew Obus},
journal= {arXiv preprint arXiv:1109.4776},
year = {2015}
}
Comments
Final version, to appear in Proc. Amer. Math. Soc. Still 11 pages