Sur le sous-groupe des \'el\'ements de hauteur infinie du K2 d'un corps de nombres

TL;DR

This paper computes the 2-rank of the wild kernel and the subgroup of infinite height elements in K2 of a number field using logarithmic methods related to class groups.

Contribution

It introduces a logarithmic approach to explicitly determine the 2-rank of specific subgroups in K2 of number fields, linking them to class groups.

Findings

Explicit formulas for 2-rank of WK2(F) and infinite height subgroup

Connection established between K2 subgroups and class groups

Applicable to any number field F

Abstract

By using the logarithmic approach of the classical kernels for the K2 of number fields, we compute the 2-rank of the wild kernel WK2(F) and the 2-rank of the subgroup of infinite heigh elements in K2(F) in terms of positive class groups for any number field F.