J. Stix proved that a curve of positive genus over 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 Rk/QX 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 cor k/Q([P]) ∈ Br (Q) is non-trivial, then X satisfies the section conjecture.
On the section conjecture and Brauer–Severi varieties
Bresciani G.
2022-01-01
Abstract
J. Stix proved that a curve of positive genus over 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 Rk/QX 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 cor k/Q([P]) ∈ Br (Q) is non-trivial, then X satisfies the section conjecture.File in questo prodotto:
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