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 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.

arXiv comment20 pages, magma code as ancillary files. final version to appear in Compositio Math

References in corpus (6)

• The Cassels-Tate pairing on polarized abelian varieties
• Derived categories of coherent sheaves on abelian varieties and equivalences between them
• Derived categories of coherent sheaves and motives
• Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields
• Moduli spaces of torsion sheaves on K3 surfaces and derived equivalences
• Failure of the Hasse principle on general K3 surfaces

Cited by in corpus (2)

• A threefold violating a local-to-global principle for rationality
• A transcendental Brauer-Manin obstruction to weak approximation on a Calabi-Yau threefold