TITLE: Obstruction and rational points on curves
QUESTION [6 upvotes]: Is etale-Brauer the only obstruction to the existence of rational points on projective plane curves over number fields?

REPLY [10 votes]: As a supplement to Daniel's answer, I'd like to mention that for (smooth projective geometrically irreducible) curves over number fields, "Brauer-Manin is the only obstruction to the existence of rational points" is a question formulated in Skorobogatov's book (page 133) and a conjecture of mine. See my paper, in particular sections 8 and 9. The statement is true when the Tate-Shafarevich group and the Mordell-Weil group of the Jacobian are both finite, see Thm. 8.6 in the paper. Poonen in this paper (Experiment. Math. 2006) has a conjecture based on heuristic considerations that would imply the general statement.