Minus class groups of the fields of the 𝑙-th roots of unity

DOI10.1090/S0025-5718-98-00939-9zbMath0902.11043OpenAlexW1974873463MaRDI QIDQ4396460

René Schoof

Publication date: 14 June 1998

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-98-00939-9

zbMATH Keywords

tablesIwasawa theorygroup cohomologyBernoulli numbersStickelberger elementsfactorization of the relative class numbersfields of the \(l\)th roots of unityminus class groups

Mathematics Subject Classification ID

Bernoulli and Euler numbers and polynomials (11B68) Class numbers, class groups, discriminants (11R29) Iwasawa theory (11R23) Software, source code, etc. for problems pertaining to number theory (11-04) Cyclotomic extensions (11R18) Galois cohomology (11R34)

Related Items

Class numbers of real cyclotomic fields of prime conductor ⋮ Class number parity of a quadratic twist of a cyclotomic field of prime power conductor ⋮ On the class groups of certain imaginary cyclic fields of 2-power degree ⋮ Anderson's module for cyclotomic fields of prime conductor ⋮ Fitting ideals of isotypic parts of even K-groups ⋮ Generating subgroups of ray class groups with small prime ideals ⋮ Relative class numbers inside the \(p\)th cyclotomic field ⋮ Fitting ideals in number theory and arithmetic ⋮ The 2-Ideal Class Groups of ℚ(ζl) ⋮ The parity of the class number of the cyclotomic fields of prime conductor ⋮ Short Stickelberger Class Relations and Application to Ideal-SVP ⋮ The structure of higher-dimensional Iwasawa modules under a far-fetched assumption ⋮ Visibility of ideal classes ⋮ Prime factors of class number of cyclotomic fields ⋮ On the 2-part of the class numbers of cyclotomic fields of prime power conductors ⋮ Isomorphism classification of Leary-Minasyan groups ⋮ Genus theory and \(\varepsilon\)-conjectures on \(p\)-class groups

Cites Work

• Class fields of abelian extensions of \(\mathbb Q\)
• Class groups of abelian fields, and the main conjecture
• On the class groups of imaginary abelian fields
• Cohomology of class groups of cyclotomic fields; an application to Morse- Smale diffeomorphisms
• Anderson's module for cyclotomic fields of prime conductor
• Prime Factors of Cyclotomic Class Numbers
• Table of the cyclotomic class numbers ℎ*(𝑝) and their factors for 200<𝑝<521
• Class Number Computations of Real Abelian Number Fields
• A Note on Ideal Class Groups
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