Genus formulas and Greenberg's conjecture

DOI10.1007/s40316-017-0093-yzbMath1423.11188OpenAlexW2766215976WikidataQ123022429 ScholiaQ123022429MaRDI QIDQ1616066

Thong Nguyen Quang Do

Publication date: 31 October 2018

Published in: Annales Mathématiques du Québec (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40316-017-0093-y

zbMATH Keywords

Iwasawa invariantsGreenberg's conjecturecyclotomic $\mathbb{Z}_p$-extensiongenus formulasunified criteria

Mathematics Subject Classification ID

Iwasawa theory (11R23)

Related Items (6)

\(p\)-adic approach of Greenberg's conjecture for totally real fields ⋮ Normes universelles et conjecture de Greenberg ⋮ Abelian prinicipalization of groups of logarithmic classes ⋮ Algorithmic complexity of Greenberg's conjecture ⋮ Tamely ramified Iwasawa modules having no non-trivial pseudo-null submodules ⋮ Ideal norms in the cyclotomic tower and Greenberg's conjecture

Uses Software

• PARI/GP

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Iwasawa descent and co-descent for units modulo circular units. With an appendix by J.-R. Belliard.
• On the Stickelberger ideal and the circular units of an abelian field
• Regulators and Iwasawa modules
• Unités cyclotomiques, unités semilocales et \(\mathbb{Z}_\ell\)-extensions. II
• On \(p\)-adic zeta functions and \(\mathbb{Z}_p\)-extensions of certain totally real number fields
• The class group of \(\mathbb{Z}_p\)-extensions over totally real number fields
• \(p\)-adic approach of Greenberg's conjecture for totally real fields
• On mirror equalities and certain weak forms of Greenberg's conjecture
• Logarithmic classes of number fields
• On \(\mathbb Z_{\ell}\)-extensions of algebraic number fields
• A note on the capitulation in \(\mathbb{Z}_ p\)-extensions
• On the cyclotomic norms and the Leopoldt and Gross-Kuz'min conjectures
• Sur une forme faible de la conjecture de Greenberg II
• On Cohomology Groups of Units for Z p -Extensions
• On the Iwasawa Invariants of Totally Real Number Fields
• A note on the ideal class group of the cyclotomic Z_p-extension of a totally real number field
• On Modified Circular Units and Annihilation of real Classes
• Sous-modules d'unit\'es en th\'eorie d'Iwasawa
• ON THE THETA SERIES ATTACHED TO $D_{m}^{+}$–LATTICES
• THE TATE MODULE FOR ALGEBRAIC NUMBER FIELDS
• On capitulation cokernels in Iwasawa theory
• On capitulation of \(S\)-ideals in \(\mathbb{Z}_p\)

This page was built for publication: Genus formulas and Greenberg's conjecture