… In Section 5 we apply Theorem 1.1 to describe exact functors between the abelian
categories of twisted coherent sheaves. In particular we deduce a Gabriel-type result for twisted …

… Generally not every morphism of FourierMukai functors is induced by a morphism of their
kernels, but something like the adjunction counit (1.4) one does expect to come from some …

… If the Fourier–Mukai functor is an equivalence we will call it a Fourier–Mukai transform. …
However, from the uniqueness of the kernel of a twisted Fourier–Mukai transform we conclude …

… If the Fourier–Mukai functor is an equivalence we will call it a Fourier–Mukai transform. …
However, from the uniqueness of the kernel of a twisted Fourier– Mukai transform we conclude …

… Suppose that R Φ and R Φ form a pair of functors which are of Fourier-Mukai type. Then n —
r, … If we apply R Φ to the structure sequence of S twisted by ^ then we obtain the long exact …

… between derived categories of coherent sheaves is said to be a Fourier–Mukai functor if it
is … on twisted sheaves on complex manifolds. In Section 8, we introduce Fourier–Mukai …

… Notice that the twisting functor ⊗L is obtained in our picture as CorF (Ψ(01)[−1]). Also for any
symmetric form q on Zk+1 with the properties |q(ei,ei+1)| = 1 for any i, q(ei,ej) = 0 for |i−j| > 1, …

… Taking the twist of a functor is completely general and does not in itself rely on the fact that …
twist of a Fourier–Mukai transform we need a natural choice of the morphism of Fourier–Mukai …

… functor for it to be still isomorphic to a Fourier–Mukai functor, ie of the form (1) but not necessarily
fully faithful. The condition is in particular satisfied if the functor … E}\) and twisting by n we …

… These functors were investigated by Mukai [39,41] in various cases: for example, when X …
categories, and the functors are then known as Fourier–Mukai transforms. This phenomenon is …