Universal Brauer-Severi varieties

TL;DR

This paper constructs and studies universal Brauer-Severi varieties, analyzing their geometric and cohomological properties, and applies these findings to reinterpret a key result in algebraic geometry.

Contribution

It introduces the concept of universal Brauer-Severi varieties with fixed period and index, and explores their geometry, cohomology, and fundamental groups, providing new insights and applications.

Findings

Determined cohomology, Brauer, and Picard groups of these varieties.

Showed they are almost always simply connected.

Reinterpreted the discriminant avoidance result of de Jong and Starr.

Abstract

We construct universal Brauer-Severi varieties of fixed period and index and study their geometry. We determine their cohomology and their Brauer and Picard groups and show that they are almost always simply connected. As an application, we reinterpret the discriminant avoidance result of de Jong and Starr in terms of universal Brauer-Severi varieties.