Derived categories of torsors for abelian schemes

Benjamin Antieau*, Daniel Krashen, Matthew Ward

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

In the first part of our paper, we show that there exist non-isomorphic derived equivalent genus 1 curves, and correspondingly there exist non-isomorphic moduli spaces of stable vector bundles on genus 1 curves in general. Neither occurs over an algebraically closed field. We give necessary and sufficient conditions for two genus 1 curves to be derived equivalent, and we go on to study when two principal homogeneous spaces for an abelian variety have equivalent derived categories. We apply our results to study twisted derived equivalences of the form Db(J,α)≃Db(J,β), when J is an elliptic fibration, giving a partial answer to a question of Căldăraru.

Original languageEnglish (US)
Pages (from-to)1-23
Number of pages23
JournalAdvances in Mathematics
Volume306
DOIs
StatePublished - Jan 14 2017
Externally publishedYes

Keywords

  • Brauer groups
  • Derived equivalence
  • Elliptic 3-folds
  • Genus 1 curves

ASJC Scopus subject areas

  • Mathematics(all)

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