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arXiv · 1109.4776

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

Andrew Obus
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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.

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Andrew Obus. 2012-09-07. Conductors of wild extensions of local fields, especially in mixed characteristic (0,2). https://arxiv.org/abs/1109.4776

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