Abstract
A celebrated result by Orlov states that any fully faithful exact functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of geometric origin, i.e. it is a Fourier–Mukai functor. In this paper we prove that any smooth projective variety of dimension ≥ 3 equipped with a tilting bundle can serve as the source variety of a non-Fourier–Mukai functor between smooth projective schemes.
| Original language | English |
|---|---|
| Pages (from-to) | 1254-1267 |
| Number of pages | 14 |
| Journal | Compositio Mathematica |
| Volume | 158 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - 12 Aug 2022 |
Bibliographical note
Funding Information:We would like to thank the referees for the thorough reading of the manuscript and for the useful suggestions and comments which have helped us to improve the paper. The first author is supported by a postdoctoral fellowship from the Research Foundation – Flanders (FWO). The second author is a Lecturer at the University of Liverpool and at the time of writing, she was supported by EPSRC grant EP/N021649/1. The third author is a senior researcher at the Research Foundation – Flanders (FWO). At the time of writing, he was supported by the FWO-grant G0D8616N ‘Hochschild cohomology and deformation theory of triangulated categories.’
Funding Information:
The first author is supported by a postdoctoral fellowship from the Research Foundation – Flanders (FWO). The second author is a Lecturer at the University of Liverpool and at the time of writing, she was supported by EPSRC grant EP/N021649/1. The third author is a senior researcher at the Research Foundation – Flanders (FWO). At the time of writing, he was supported by the FWO-grant G0D8616N ‘Hochschild cohomology and deformation theory of triangulated categories.’
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© 2022 The Author(s).
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