Rational points and derived equivalence

Nicolas Addington; Benjamin Antieau; Katrina Honigs; Sarah Frei

doi:10.1112/S0010437X21007089

Rational points and derived equivalence

Nicolas Addington, Benjamin Antieau, Katrina Honigs, Sarah Frei

Mathematics

Research output: Contribution to journal › Article › peer-review

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)
Pages (from-to)	1036-1050
Number of pages	15
Journal	Compositio Mathematica
DOIs	https://doi.org/10.1112/S0010437X21007089
State	Accepted/In press - 2021

Keywords

Brauer-Manin obstructions
derived categories of coherent sheaves
holomorphic symplectic varieties
K3 surfaces
moduli spaces of sheaves
rational points

ASJC Scopus subject areas

Algebra and Number Theory

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10.1112/S0010437X21007089

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AU - Addington, Nicolas

AU - Antieau, Benjamin

AU - Honigs, Katrina

AU - Frei, Sarah

N1 - Publisher Copyright: © The Author(s) 2021.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Brauer-Manin obstructions

KW - derived categories of coherent sheaves

KW - holomorphic symplectic varieties

KW - K3 surfaces

KW - moduli spaces of sheaves

KW - rational points

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Rational points and derived equivalence

Abstract

Keywords

ASJC Scopus subject areas

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