Rational points and derived equivalence
Abstract
We give the first examples of derived equivalences between varieties defined over non-closed fields where one has a rational point and the other does not. We begin with torsors over Jacobians of curves over Q and Fq(t), and conclude with a pair of hyperkaehler 4-folds over Q. The latter is independently interesting as a new example of a transcendental Brauer-Manin obstruction to the Hasse principle.
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