Rational points and derived equivalence
Algebraic Geometry
2021-07-01 v2 Number Theory
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.
Cite
@article{arxiv.1906.02261,
title = {Rational points and derived equivalence},
author = {Nicolas Addington and Benjamin Antieau and Sarah Frei and Katrina Honigs},
journal= {arXiv preprint arXiv:1906.02261},
year = {2021}
}
Comments
20 pages, magma code as ancillary files. final version to appear in Compositio Math