TY - JOUR
T1 - An example of a non-Fourier–Mukai functor between derived categories of coherent sheaves
AU - Rizzardo, Alice
AU - Van den Bergh, Michel
AU - Neeman, Amnon
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
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.
UR - http://www.scopus.com/inward/record.url?scp=85061029922&partnerID=8YFLogxK
U2 - 10.1007/s00222-019-00862-9
DO - 10.1007/s00222-019-00862-9
M3 - Article
SN - 0020-9910
VL - 216
SP - 927
EP - 1004
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 3
ER -