Anderson's module for cyclotomic fields of prime conductor

DOI10.1006/jnth.1997.2184zbMath0888.11045OpenAlexW2007074462MaRDI QIDQ1377599

Pietro Cornacchia

Publication date: 27 May 1998

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2184

zbMATH Keywords

unitscyclotomic fieldGalois cohomologyclass groupscyclotomic unitsTate cohomologyStickelberger idealminus class groupAnderson's moduleplus class groupStickelberger quotient

Mathematics Subject Classification ID

Class numbers, class groups, discriminants (11R29) Cyclotomic extensions (11R18) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

Related Items (6)

Class numbers of real cyclotomic fields of prime conductor ⋮ Greenberg’s conjecture for real quadratic fields and the cyclotomic ℤ₂-extensions ⋮ A NOTE ON THE EQUIVALENCE OF THE PARITY OF CLASS NUMBERS AND THE SIGNATURE RANKS OF UNITS IN CYCLOTOMIC FIELDS ⋮ The 2-Ideal Class Groups of ℚ(ζl) ⋮ Minus class groups of the fields of the 𝑙-th roots of unity ⋮ Fitting ideals of class groups of real fields with prime power conductor

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
• Global units and ideal class groups
• On the structure of relative class groups. With an appendix of numerical examples
• Another look at the index formulas of cyclotomic number theory
• On the Dimension of Modules and Algebras, II: (Frobenius Algebras and Quasi-Frobenius Rings)
• The parity of the class number of the cyclotomic fields of prime conductor
• Minus class groups of the fields of the 𝑙-th roots of unity
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