Rational points and derived equivalence

Nicolas Addington, Benjamin Antieau, Katrina Honigs, Sarah Frei

Research output: Contribution to journalArticlepeer-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 languageEnglish (US)
Pages (from-to)1036-1050
Number of pages15
JournalCompositio Mathematica
DOIs
StateAccepted/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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