Essential p-dimension of algebraic groups whose connected component is a torus

TL;DR

This paper investigates the essential p-dimension of certain algebraic groups with a torus as their connected component, building on previous research by Karpenko and Merkurjev.

Contribution

It provides new insights into the essential p-dimension of algebraic groups with torus-connected components, extending prior work in the field.

Findings

Determined the essential p-dimension for specific classes of algebraic groups.

Extended existing formulas to broader classes of groups.

Connected the essential p-dimension to properties of the torus component.

Abstract

Following up on our earlier work and the work of N. Karpenko and A. Merkurjev, we study the essential p-dimension of linear algebraic groups G whose connected component G^0 is a torus.