Solvable Number Field Extensions of Bounded Root Discriminant

2011/11/23 by Leshin, Jonah · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1111.5651

Abstract

Let K be a number field and d_K the absolute value of the discrimant of K/ℚ. We consider the root discriminant d_L^{(1)/([L: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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