Non-split Brauer-Severi varieties do not admit full exceptional collections

TL;DR

This paper discusses a conjecture about non-split Brauer-Severi varieties and shows how a stronger version can be derived from existing results on noncommutative motives.

Contribution

It demonstrates that a stronger form of Novaković's conjecture follows from known results, advancing understanding of derived categories of these varieties.

Findings

A stronger version of the conjecture is supported by known noncommutative motives results.

Non-split Brauer-Severi varieties do not admit full strong exceptional collections.

The connection between motives and derived categories is clarified.

Abstract

Recently, Novakovi\'c conjectured that non-split Brauer-Severi varieties do not admit full strong exceptional collections. In this short note, we explain how a stronger version of this conjecture follows easily from known results on noncommutative motives.