Computation of 2-groups of positive classes of exceptional number fields

TL;DR

This paper introduces an algorithm to compute the 2-group of positive divisor classes in certain number fields with exceptional dyadic places, and applies it to determine the 2-rank of the wild kernel in K2(F).

Contribution

The paper presents a novel algorithm for computing positive divisor class groups in number fields with exceptional dyadic places, advancing computational number theory.

Findings

Successfully computed the 2-rank of WK2(F) for specific number fields.

Demonstrated the effectiveness of the algorithm in cases with exceptional dyadic places.

Abstract

We present an algorithm for computing the 2-group of the positive divisor classes of a number field F in case F has exceptional dyadic places. As an application, we compute the 2-rank of the wild kernel WK2(F) in K2(F) for such number fields.