Novaković's conjecture on exceptional collections on non-split Brauer–Severi varieties

Let $k$ be a field and let $X\neq \mathbb{P}_k^n$ be an $n$-dimensional Brauer–Severi variety. Write $D^b(X)$ for its bounded derived category of coherent sheaves.

Novaković's conjecture. $D^b(X)$ does not admit a full strongly exceptional collection.

The conjecture strengthens the assertion that non-split Brauer–Severi varieties do not admit full strong exceptional collections. The paper explains that this stronger form follows from known results on noncommutative motives.