Class Field Towers and Root Discriminants

Details Class Field Towers and Root Discriminants Class Field Towers and Root Discriminants

2011-11-23

arxiv.org/abs/1111.5651v3

Mathematics

Number Theory

Scientific paper

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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