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 \({\text {cor}}_{k/\mathbb {Q}}([P])\in {\text {Br}}(\mathbb {Q})\) is non-trivial, then X satisfies the section conjecture.

J. Stix 证明了映射到非平凡 Brauer-Severi 变体的\(\mathbb {Q}\)上的正属曲线满足截面猜想。我们证明，如果X是数域k 上的正属曲线，并且 Weil 限制\(R_{k/\mathbb {Q}}X\)允许有理映射到非平凡的 Brauer-Severi 变体，则X满足截面猜想。因此，如果X映射到 Brauer-Severi 变体P使得核心约束\({\text {cor}}_{k/\mathbb {Q}}([P])\in {\text {Br} }(\mathbb {Q})\)是非平凡的，则X满足截面猜想。