  We study homotopy rational points of Brauer-Severi varieties over fields of
characteristic zero. We are particularly interested if a Brauer-Severi variety
admitting a homotopy rational point splits. The analogue statement turns out to
be true for open subvarieties of twisted hyperplane arrangements. In the
complete case, the obstruction turns out to be the pullback of the Chern class
of a generator of the Picard group along the homotopy rational point. Moreover,
we will show that every Brauer-Severi variety over a $p$-adic field with
$p$-primary period admits a homotopy rational point.
