The Rank of the 2-Class Group of Some Fields with Large Degree

ALGEBRA COLLOQUIUM（2022）

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摘要

Let n >= 3 be an integer and d an odd square-free integer. We compute the rank of the 2-class group of some fields of the form L-n,L-d = Q(zeta(2n), root d) when all the prime divisors of d are congruent to +/- 3 (mod 8) or 9 (mod 16).

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关键词

cyclotomic Z(2)-extension, 2-rank, 2-class group

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