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Solvable number field extensions of bounded root discriminant


Author: Jonah Leshin
Journal: Proc. Amer. Math. Soc. 141 (2013), 3341-3352
MSC (2010): Primary 11R20, 11R29; Secondary 11-XX
DOI: https://doi.org/10.1090/S0002-9939-2013-12015-0
Published electronically: June 14, 2013
MathSciNet review: 3080157
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ K$ be a number field and $ d_K$ the absolute value of the discriminant of $ K/\mathbb{Q}$. We consider the root discriminant $ d_L^{\frac {1}{[L:\mathbb{Q}]}}$ of extensions $ L/K$. We show that for any $ N>0$ and any positive integer $ n$, the set of length $ n$ solvable extensions of $ K$ with root discriminant less than $ N$ is finite. The result is motivated by the study of class field towers.


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Additional Information

Jonah Leshin
Affiliation: Department of Mathematics, Brown University, 151 Thayer Street, Providence, Rhode Island 02912
Email: JLeshin@math.brown.edu

DOI: https://doi.org/10.1090/S0002-9939-2013-12015-0
Received by editor(s): December 12, 2011
Published electronically: June 14, 2013
Communicated by: Matthew A. Papanikolas
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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