On the ideal class groups of the maximal real subfields of number fields with all roots of unity

DOI10.1007/PL00011159zbMath0949.11055OpenAlexW2084003094MaRDI QIDQ1280733

Masato Kurihara

Publication date: 18 March 1999

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/pl00011159

zbMATH Keywords

Galois cohomologyIwasawa theoryclass groupsGreenberg's conjectureexistence of infinitely many real abelian extensionsmaximal real subfields

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23) Galois cohomology (11R34) Totally real fields (11R80)

Related Items (13)

Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions ⋮ PRINCIPALIZATION OF IDEALS IN ABELIAN EXTENSIONS OF NUMBER FIELDS ⋮ On the λ-stability of p-class groups along cyclic p-towers of a number field ⋮ On some local-global principles for linear algebraic groups over infinite algebraic extensions of global fields ⋮ Ideal class groups of CM-fields with non-cyclic Galois action ⋮ The Chevalley-Herbrand formula and the real abelian Main Conjecture (new criterion using capitulation of the class group) ⋮ On the ideal class groups of the maximal cyclotomic extensions of algebraic number fields ⋮ Abelian capitulation of ray class groups ⋮ Visibility of ideal classes ⋮ Abelian prinicipalization of groups of logarithmic classes ⋮ On minus quotients of ideal class groups of cyclotomic fields ⋮ Correction to: Stickelberger ideals and fitting ideals of class groups for abelian number fields ⋮ On infinite extensions of Dedekind domains, upper semicontinuous functions and the ideal class semigroups

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