On fields of definition of arithmetic Kleinian reflection groups

TL;DR

This paper proves that the degrees of the real fields of definition for arithmetic Kleinian reflection groups are bounded by 35, providing a significant restriction on their possible algebraic structures.

Contribution

It establishes an explicit upper bound on the degrees of real fields of definition for these groups, advancing understanding of their algebraic properties.

Findings

Degrees of real fields are bounded by 35.

Restricts possible algebraic structures of arithmetic Kleinian reflection groups.

Provides a new constraint for classification of these groups.

Abstract

We show that degrees of the real fields of definition of arithmetic Kleinian reflection groups are bounded by 35.