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 and, and conclude with a pair of hyperkähler 4-folds over. 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.
Original language | English (US) |
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Pages (from-to) | 1036-1050 |
Number of pages | 15 |
Journal | Compositio Mathematica |
DOIs | |
State | Accepted/In press - 2021 |
Keywords
- Brauer-Manin obstructions
- K3 surfaces
- derived categories of coherent sheaves
- holomorphic symplectic varieties
- moduli spaces of sheaves
- rational points
ASJC Scopus subject areas
- Algebra and Number Theory