Semi-local units modulo cyclotomic units

DOI10.1006/jnth.1999.2398zbMath0948.11042OpenAlexW2146735985MaRDI QIDQ1306691

Takae Tsuji

Publication date: 20 November 2000

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

Full work available at URL: https://doi.org/10.1006/jnth.1999.2398

zbMATH Keywords

cyclotomic units\(\mathbb{Z}_p\)-cyclotomic extensiongroup of semi-local units

Mathematics Subject Classification ID

Integral representations (11S23) Iwasawa theory (11R23) Integral representations related to algebraic numbers; Galois module structure of rings of integers (11R33)

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On Sharifi’s conjecture: Exceptional case ⋮ CONOYAUX DE CAPITULATION ET MODULES D'IWASAWA ⋮ Les nombres de Tamagawa locaux et la conjecture de Bloch et Kato pour les motifs sur un corps abélien ⋮ Class number parity of a quadratic twist of a cyclotomic field of prime power conductor ⋮ On the higher Fitting ideals of Iwasawa modules of ideal class groups over real abelian fields ⋮ Isotypical indices of cyclotomic elements ⋮ On the Iwasawa \(\lambda\)-invariant of the cyclotomic \(\mathbb{Z}_2\)-extension of \(\mathbb{Q}(\sqrt{p})\). III. ⋮ On tamely ramified Iwasawa modules for the cyclotomic \(\mathbb {Z}_{p}\)-extension of abelian fields ⋮ Formules de classes pour les corps abéliens réels. (Class formulae for real Abelian fields) ⋮ Hilbert-Speiser number fields and the complex conjugation ⋮ On the Iwasawa 𝜆-invariants of real abelian fields ⋮ On higher fitting ideals of certain Iwasawa modules associated with Galois representations and Euler systems ⋮ On first layers of \(\mathbb Z_p\)-extensions ⋮ On duality and Iwasawa descent ⋮ On the 2-part of the class numbers of cyclotomic fields of prime power conductors ⋮ ASYMPTOTIC COHOMOLOGY OF CIRCULAR UNITS ⋮ Ichimura-Sumida criterion for Iwasawa \(\lambda\)-invariants ⋮ Semilocal units modulo Gauss sums.

Cites Work

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• Class groups of abelian fields, and the main conjecture
• On the class groups of imaginary abelian fields
• Division values in local fields
• The Iwasawa invariant \(\mu_p\) vanishes for abelian number fields
• On the Stickelberger ideal and the circular units of an abelian field
• Unités cyclotomiques, unités semilocales et \(\mathbb{Z}_\ell\)-extensions. II
• On some modules in the theory of cyclotomic fields
• Local Units Modulo Circular Units

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