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Schoof, René

Infinite class field towers of quadratic fields. (English) Zbl 0589.12011

J. Reine Angew. Math. 372, 209-220 (1986).

In this paper we establish the existence of infinitely many quadratic number fields, both real and complex, which have an infinite class field tower and only two finite ramified primes over \({\mathbb{Q}}\). By generalizing a result of H. Koch and B. B. Venkov [Astérisque 24/25, 57- 67 (1975; Zbl 0335.12021)], we obtain some examples of quadratic fields, both real and complex, which have only one finite prime ramified over \({\mathbb{Q}}\) and yet an infinite class field tower.

Cited in 3 Reviews

Cited in 19 Documents

MSC:

11R37	Class field theory
11R11	Quadratic extensions
11R34	Galois cohomology

Keywords:

p-groups; cohomology; quadratic number fields; infinite class field tower

Citations:

Zbl 0335.12021

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