Remark on a Characterization of Certain Ring Class Fields by Their Absolute Galois Group
نویسنده
چکیده
where A(co) stands for the discriminant of the complex lattice generated by 1 and to and g2(u) is the Weierstrass invariant of this lattice. If ti=Q(\/ — D) is an imaginary quadratic number field, it is well known from the theory of class fields with complex multiplication that the "singular values" j(a), where a£û, la >0, generate algebraic number fields which are abelian over fi, namely the so-called ring class fields. Detailed references for the literature on the theory of ring class fields may be found in the report of Deuring [l]. In the rather extensive theory of ring class fields it is shown that ®Uia))/Q iS a normal extension with its Galois group © being an extension of the abelian Galois group ß of Q(j(a))/Çl, completely determined by the relations
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