Genus theory of p-adic pseudo-measures -- Tame kernels and abelian p-ramification - Archive ouverte HAL Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2023

Genus theory of p-adic pseudo-measures -- Tame kernels and abelian p-ramification

Résumé

We consider, for real abelian fields K, the Birch--Tate formula linking the tame kernel #K_2(Z_K) to ζ_K(-1); we compare, for quadratic and cyclic cubic fields with p=2,3, #K_2(\BZ_K)[p^∞] to the order of the torsion group T_{K, p} of abelian p-ramification theory given by the residue of ζ_{K, p}(s) at s=1. This is done via the ``genus theory'' of p-adic pseudo-measures, inaugurated in the 1970/80's and the fact that T_{K, p} only depends on the p-class group and on the normalized p-adic regulator of K (Theorem A). We apply this to prove a conjecture of Deng--Li giving the structures of K_2(Z_K)[2^∞] for an interesting family of real quadratic fields (Theorem B). Then, for p>3, we give a lower bound of the p-rank of K_2(\BZ_K) in cyclic p-extensions (Theorem C). Complements, PARI programs and tables are given in an Appendix.
Fichier principal
Vignette du fichier
K2-New.pdf (502.86 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-04237257 , version 1 (11-10-2023)
hal-04237257 , version 2 (17-01-2024)

Identifiants

Citer

Georges Gras. Genus theory of p-adic pseudo-measures -- Tame kernels and abelian p-ramification. 2023. ⟨hal-04237257v2⟩
32 Consultations
15 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More