Genus theory and \(\varepsilon\)-conjectures on \(p\)-class groups

DOI10.1016/j.jnt.2019.07.008zbMath1436.11134arXiv1903.02922OpenAlexW2920982518WikidataQ122937747 ScholiaQ122937747MaRDI QIDQ2329282

Georges Gras

Publication date: 17 October 2019

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

Full work available at URL: https://arxiv.org/abs/1903.02922

zbMATH Keywords

class groupsgenus theory\(p\)-ramificationclass-field theory\(\varepsilon\)-conjectures

Mathematics Subject Classification ID

Class field theory (11R37) Class numbers, class groups, discriminants (11R29) Other abelian and metabelian extensions (11R20)

Related Items (3)

ℓ-torsion bounds for the class group of number fields with an ℓ-group as Galois group ⋮ Unnamed Item ⋮ The Chevalley-Herbrand formula and the real abelian Main Conjecture (new criterion using capitulation of the class group)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Maximal class numbers of CM number fields
• Unités et classes dans les extensions metabéliennes de degrè \(n\ell^s\) sur un corps de nombres algébriques
• Global \(\ell\)-adique clean field theory
• Reflexion theorems
• Sur les \(\ell\)-classes d'idéaux dans les extensions cycliques rélatives de degré premier \(\ell\). I
• Genus theory and governing fields
• A class group heuristic based on the distribution of 1-eigenspaces in matrix groups
• Average bounds for the \(\ell\)-torsion in class groups of cyclic extensions
• Invariant generalized ideal classes -- structure theorems for \(p\)-class groups in \(p\)-extensions
• Sur les \(\ell\)-classes d'idéaux dans les extensions cycliques rélatives de degré premier \(\ell\). II
• Lesθ-régulateurs locaux d'un nombre algébrique : Conjecturesp-adiques
• On the Distribution of Class Groups of Number Fields
• The p-adic Kummer–Leopoldt constant: Normalized p-adic regulator
• Non-abelian number fields with very large class numbers
• Extreme Values of Class Numbers of Real Quadratic Fields
• Computing Arakelov class groups
• Minus class groups of the fields of the 𝑙-th roots of unity
• Bounds for the ℓ-torsion in class groups
• Heuristics and conjectures in the direction of a $p$-adic Brauer–Siegel Theorem
• Class numbers of real cyclotomic fields of prime conductor
• Rédei-matrices and applications
• On the Brun–Titchmarsh theorem
• The Cohen–Lenstra heuristics, moments and p^j-ranks of some groups
• Reflection Principles and Bounds for Class Group Torsion
• The Genus Field and Genus Number in Algebraic Number Fields
• The genus field and genus group in finite number fields
• THE GENERALIZATION OF A THEOREM OF L. RÉDEI'S

This page was built for publication: Genus theory and \(\varepsilon\)-conjectures on \(p\)-class groups