Computation of 2-groups of narrow logarithmic divisor classes of number fields

TL;DR

This paper introduces an algorithm to compute the 2-group of narrow logarithmic divisor classes of degree 0 in number fields, aiding in understanding their algebraic structure and related invariants.

Contribution

The paper presents a novel algorithm for computing the 2-group of narrow logarithmic divisor classes, expanding computational tools in algebraic number theory.

Findings

Successfully computed the 2-rank of the wild kernel WK2(F) in specific cases

Demonstrated the algorithm's effectiveness on various number fields

Enhanced understanding of the structure of narrow logarithmic divisor class groups

Abstract

We present an algorithm for computing the 2-group of narrow logarithmic divisor classes of degree 0 for number fields F. As an application, we compute in some cases the 2-rank of the wild kernel WK2(F).