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

Alice Rizzardo; Michel Van den Bergh; Amnon Neeman

doi:10.1007/s00222-019-00862-9

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

Alice Rizzardo, Michel Van den Bergh^*, Amnon Neeman

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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 language	English
Pages (from-to)	927-1004
Number of pages	78
Journal	Inventiones Mathematicae
Volume	216
Issue number	3
DOIs	https://doi.org/10.1007/s00222-019-00862-9
Publication status	Published - 1 Jun 2019

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abstract = "Orlov{\textquoteright}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.",

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AB - 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.

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

Abstract

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