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arXiv · 1906.02261

Rational points and derived equivalence

Nicolas Addington·Benjamin Antieau·Sarah Frei·Katrina Honigs
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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 F_q(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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Nicolas Addington, Benjamin Antieau, Sarah Frei, Katrina Honigs. 2019-06-05. Rational points and derived equivalence. https://doi.org/10.1112/s0010437x21007089

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