Kaplansky Unit conjecture for complex numbers

TL;DR

This paper proves Kaplansky's unit conjecture for group rings over the complex numbers, confirming a long-standing algebraic hypothesis in this specific setting.

Contribution

The paper establishes the validity of Kaplansky's unit conjecture specifically for complex number fields, providing a significant theoretical advancement.

Findings

Kaplansky's unit conjecture holds over complex numbers.

The proof confirms the conjecture in this specific algebraic context.

This result narrows the gap in understanding the conjecture's validity across different fields.

Abstract

We show that Kaplansky's unit conjecture is true, under the assumption that the underlying field is complex.