Versal Family of Reductive Groups

TL;DR

This paper constructs a comprehensive family of reductive groups, including quasi-split variants, providing a systematic framework for studying their invariants up to a certain rank.

Contribution

It introduces a versal family of reductive groups that encompasses all groups up to a given rank, extending previous results and enabling systematic analysis.

Findings

Constructed a versal family of reductive groups including all up to a certain rank.

Extended previous work by N.Avni and R.Aizenbud.

Provides a framework for studying invariants of bounded rank reductive groups.

Abstract

In this paper, we construct a family of reductive groups, including all reductive groups up to a given rank. We also construct a similar versal family of quasi-split reductive groups. This result generalizes a former result of N.Avni and R.Aizenbud and provides a framework for systematically studying invariants of reductive groups with bounded rank.