An example of a non-Fourier-Mukai functor between derived
categories of coherent sheaves
-- Michel van den Bergh, May 1, 2015

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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. We show that this result
is false without the full faithfulness hypothesis. This is
joint work with Alice Rizzardo.