Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields

On the maximal unramified pro-2-extension of Z2-extensions of certain real quadratic fields II

“…In [17], it has been proved that λ(K) = µ(K) = ν(K) = 0, i.e., L(K ∞ ) = K ∞ . (As in [17], we can see that #A(K 1 ) = 1 by Theorem 5.6 of [6]. By using Theorem 1 of [7], we get…”

Der Briefwechsel Hasse - Scholz - Taussky

“…• Die von Tschebotareff initiierte und von Scholz ausgebaute Theorie der Geschlechter-und Zentralklassenkörper wurde von Fröhlich [79] ein zweites Mal entwickelt.…”

genus theory for function fields

“…Then we get the following proposition. PROPOSITION The rest is the same as in the classical case [2]. …”

“…with a fixed place oo of degree d. Let £(oo) be the residue field at oo. Fix a sign function (see [5] for definitions) sgn : K^ -* fc(oo) SunghanBae and Ja Kyung Koo [2] where AT^ is the completion of K at oo and a n uniformizer at oo with sgn(7r) = 1. In applications K x replaces K, so we need an analog of the field of complex numbers C. Define C = K^ ((-n) lKqd~X) ).…”

“…In 1951, Hasse introduced genus theory of quadratic number fields [3]. Later, Frohlich generalized the theory to arbitrary number fields [2].…”