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

Access to Document

10.1016/j.aim.2015.05.013

1402.4506v2Accepted author manuscript, 392 KB

Fingerprint Dive into the research topics of 'Scalar extensions of derived categories and non-Fourier-Mukai functors'. Together they form a unique fingerprint.

Cite this

@article{4ca7e1526f3142beb4f9b337e9a85ebd,

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. ",

author = "Alice Rizzardo and {Van den Bergh}, Michel",

year = "2015",

month = aug,

doi = "10.1016/j.aim.2015.05.013",

language = "English",

pages = "1100--1144",

journal = "Advances in Mathematics",

issn = "0001-8708",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Scalar extensions of derived categories and non-Fourier-Mukai functors

AU - Rizzardo, Alice

AU - Van den Bergh, Michel

PY - 2015/8

Y1 - 2015/8

N2 - 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.

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.

U2 - 10.1016/j.aim.2015.05.013

DO - 10.1016/j.aim.2015.05.013

M3 - Article

SP - 1100

EP - 1144

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -