Finite subgroups of automorphism groups of Severi--Brauer varieties

Abstract: We classify finite subgroups of automorphism groups of non-trivial Severi--Brauer varieties of dimension $p-1$, where $p \ge 3$ is prime, over an arbitrary field whose characteristic is coprime to $p$. In addition, we construct a universal example in the case when the base field has characteristic 0; that is, we exhibit a field of characteristic 0 together with a non-trivial Severi--Brauer variety such that every finite subgroup allowed by our classification acts on it. For positive characteristic, we provide universal examples in a weaker sense.