Valuative characterization of central extensions of algebraic tori on Krull domains

TL;DR

This paper characterizes finite central extensions of algebraic tori using ramification theory of regular actions on Krull algebras over algebraically closed fields, providing a new perspective on their structure.

Contribution

It introduces a valuative approach to classify central extensions of algebraic tori via ramification theory on Krull domains, extending previous understanding.

Findings

Finite central extensions are characterized by ramification data.

The approach applies to fields of any characteristic.

Provides a new framework for understanding algebraic torus extensions.

Abstract

For an algebraic torus $T$, the finite central extensions $G$ of $T$ are characterized in terms of ramification theory of regular actions of $G$ on Krull algebras over an algebraically closed base field $K$ of any characteristic.