  J. Stix proved that a curve of positive genus over $\mathbb{Q}$ which maps to
a non-trivial Brauer-Severi variety satisfies the section conjecture. We prove
that, if $X$ is a curve of positive genus over a number field $k$ and the Weil
restriction $R_{k/\mathbb{Q}}X$ admits a rational map to a non-trivial
Brauer-Severi variety, then $X$ satisfies the section conjecture. As a
consequence, if $X$ maps to a Brauer-Severi variety $P$ such that the
corestriction
$\operatorname{cor}_{k/\mathbb{Q}}([P])\in\operatorname{Br}(\mathbb{Q})$ is
non-trivial, then $X$ satisfies the section conjecture.

Number Theory;Algebraic Geometry