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arXiv · 1111.5651

Solvable Number Field Extensions of Bounded Root Discriminant

Jonah Leshin
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Abstract

Let $K$ be a number field and $d_K$ the absolute value of the discrimant 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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Jonah Leshin. 2011-11-23. Solvable Number Field Extensions of Bounded Root Discriminant. https://arxiv.org/abs/1111.5651

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