Scalar extensions of derived categories and non-Fourier-Mukai functors

Alice Rizzardo, Michel Van den Bergh

Research output: Contribution to journalArticlepeer-review

Abstract

Orlov's famous representability theorem asserts that any fully faithful functor between the derived categories of coherent sheaves on smooth projective varieties is a Fourier-Mukai functor. This result has been extended by Lunts and Orlov to include functors from perfect complexes to quasi-coherent complexes. In this paper we show that the latter extension is false without the full faithfulness hypothesis. Our results are based on the properties of scalar extensions of derived categories, whose investigation was started by Pawel Sosna and the first author.
Original languageEnglish
Pages (from-to)1100-1144
JournalAdvances in Mathematics
Early online date17 Jun 2015
DOIs
Publication statusPublished - Aug 2015
Externally publishedYes

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