A modular curve $X/\Q$ has a local obstruction (to rational points) if it has no real points, or if it has no $\Q_p$-points for some prime $p$.
When $X$ has genus $0$ the absence of local obstructions guarantees the existence of rational points, but this is not true in general.
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- Last edited by Andrew Sutherland on 2023-07-05 15:22:20
- 2023-07-05 15:22:20 by Andrew Sutherland
- 2023-07-05 15:20:34 by Andrew Sutherland
- 2023-07-05 15:20:22 by Andrew Sutherland