Conductors of wild extensions of local fields, especially in mixed characteristic (0,2)

Details Conductors of wild extensions of local fields, especially in mixed characteristic (0,2) Conductors of wild extensions of local fields, especially in mixed characteristic (0,2)

2011-09-22

arxiv.org/abs/1109.4776v2

Mathematics

Number Theory

11 pages. This paper is a modified and expanded version of appendix C of arxiv::0911.1103v4 by the author. Version 5 of that p

Scientific paper

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.

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