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

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.

MSC:

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

Citations:

Zbl 0335.12021
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