An example of a non-Fourier–Mukai functor between derived categories of coherent sheaves

Alice Rizzardo, Michel Van Den Bergh, Amnon Neeman

Research output: Contribution to journalArticlepeer-review

Abstract

Orlov’s famous representability theorem asserts that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is a Fourier–Mukai functor. In this paper we show that this result is false without the fully faithfulness hypothesis. We also show that our functor does not lift to the homotopy category of spectral categories if the ground field is Q.
Original languageEnglish
Pages (from-to)927-1004
JournalInventiones mathematicae
Volume216
Issue number3
Early online date29 Jan 2019
DOIs
Publication statusPublished - 30 Jun 2019

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