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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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


Author: Andrew Obus
Journal: Proc. Amer. Math. Soc. 142 (2014), 1485-1495
MSC (2010): Primary 11S15, 11S20; Secondary 11R18, 11R20, 12F05, 12F10
Published electronically: February 4, 2014
MathSciNet review: 3168456
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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 of the form $ K_0(\zeta _{p^c}, \sqrt [p^c]{a})/K_0$, where $ a \in K_0(\zeta _{p^c})$. Here $ \zeta _{p^c}$ is a primitive $ p^c$th root of unity. In certain cases, including when $ a \in K_0$ and $ p=2$, we calculate the conductor exactly. These calculations can be used to determine the discriminants of various extensions of $ \mathbb{Q}$ obtained by adjoining roots of unity and radicals.


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Additional Information

Andrew Obus
Affiliation: Department of Mathematics, MC4403, Columbia University, 2990 Broadway, New York, New York 10027
Address at time of publication: Department of Mathematics, University of Virginia, P. O. Box 400137, Charlottesville, Virginia 229904-4137
Email: obus@virginia.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11881-8
Keywords: Higher ramification groups, local fields, conductor, cyclotomic extensions
Received by editor(s): October 2, 2011
Received by editor(s) in revised form: May 29, 2012
Published electronically: February 4, 2014
Additional Notes: The author was supported by an NSF Postdoctoral Research Fellowship in the Mathematical Sciences. Final preparation of this paper took place at the Max-Planck-Institut für Mathematik in Bonn
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2014 American Mathematical Society