Derived categories of torsors for abelian schemes

Benjamin Antieau, Daniel Krashen, Matthew Ward

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

Torsor
Derived Category
Genus
Curve
Elliptic Fibration
Derived Equivalence
Stable Vector Bundles
Abelian Variety
Homogeneous Space
Algebraically closed
Moduli Space
Partial
Necessary Conditions
Sufficient Conditions

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Keywords

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

Cite this

Antieau, Benjamin ; Krashen, Daniel ; Ward, Matthew. / Derived categories of torsors for abelian schemes. In: Advances in Mathematics. 2017 ; Vol. 306. pp. 1-23.
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Derived categories of torsors for abelian schemes. / Antieau, Benjamin; Krashen, Daniel; Ward, Matthew.

In: Advances in Mathematics, Vol. 306, 14.01.2017, p. 1-23.

Research output: Contribution to journalArticle

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