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

Alice Rizzardo; Michel Van den Bergh

doi:10.1016/j.aim.2015.05.013

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

Alice Rizzardo, Michel Van den Bergh

Research output: Contribution to journal › Article › peer-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 language	English
Pages (from-to)	1100-1144
Journal	Advances in Mathematics
Early online date	17 Jun 2015
DOIs	https://doi.org/10.1016/j.aim.2015.05.013
Publication status	Published - Aug 2015
Externally published	Yes

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10.1016/j.aim.2015.05.013

1402.4506v2Accepted author manuscript, 392 KB

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title = "Scalar extensions of derived categories and non-Fourier-Mukai functors",

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. ",

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AU - Van den Bergh, Michel

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AB - 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.

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JO - Advances in Mathematics

JF - Advances in Mathematics

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

Abstract

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