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Rational points and derived equivalence

Published online by Cambridge University Press:  30 April 2021

Nicolas Addington
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA adding@uoregon.edu
Benjamin Antieau
Affiliation:
Department of Mathematics, Northwestern University, 2033 Sheridan Road, Evanston, IL 60208, USA antieau@northwestern.edu
Katrina Honigs
Affiliation:
Department of Mathematics, University of Oregon, Eugene, OR 97403-1222, USA honigs@uoregon.edu
Sarah Frei
Affiliation:
Department of Mathematics, Rice University, 6100 Main Street, Houston, TX 77005-1892, USA sarah.frei@rice.edu

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 $\mathbb {Q}$ and $\mathbb {F}_q(t)$, and conclude with a pair of hyperkähler 4-folds over $\mathbb {Q}$. The latter is independently interesting as a new example of a transcendental Brauer–Manin obstruction to the Hasse principle. The source code for the various computations is supplied as supplementary material with the online version of this article.

Type
Research Article
Copyright
© The Author(s) 2021

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