Essential Dimension of Central Simple Algebras when the Characteristic is Bad

TL;DR

This paper surveys the essential dimension of central simple algebras over fields with bad characteristic, summarizing current knowledge, presenting new minor results, and highlighting open questions in the area.

Contribution

It provides a comprehensive overview of the state of the art, includes some new minor results, and discusses open problems related to essential dimension in bad characteristic.

Findings

Bounds on essential dimension are established.

Some exact values of essential dimension are identified.

Open questions remain in the area.

Abstract

This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and finite sequences of such algebras over fields whose characteristic divides the degree of the algebras under discussion. Upper and lower bounds as well as a few precise evaluations of this dimension are included.