Related papers: Fourier-Mukai functors in the supported case
We show that every exact fully faithful functor from the category of perfect complexes on the spectrum of dual numbers to the bounded derived category of a noetherian separated scheme is of Fourier-Mukai type. The kernel turns out to be an…
Due to a theorem by Orlov every exact fully faithful functor between the bounded derived categories of coherent sheaves on smooth projective varieties is of Fourier-Mukai type. We extend this result to the case of bounded derived categories…
This paper surveys some recent results about Fourier--Mukai functors. In particular, given an exact functor between the bounded derived categories of coherent sheaves on two smooth projective varieties, we deal with the question whether…
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…
We extend Orlov's result that certain functors between derived categories of smooth projective varieties are Fourier--Mukai transforms to the case when those varieties are smooth and proper.
The aim of this mainly expository note is to point out that, given an Fourier-Mukai functor, the condition making it fully faithful is an instance of \emph{generic vanishing}. We test this point of view on some fairly classical examples,…
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…
We characterise those objects in the derived category of a scheme which are a sheaf supported on a closed subscheme in terms of Koszul complexes. This is applied to generalize to arbitrary schemes the fully faithfullness criteria of an…
We extend to singular schemes with Gorenstein singularities or fibered in schemes of that kind Bondal and Orlov's criterion for an integral functor to be fully faithful. We also contemplate a criterion for equivalence. We offer a proof that…
We give a condition for an exact functor between triangulated categories to be an equivalence. Applications to Fourier-Mukai transforms are discussed. In particular, we obtain a large number of such transforms for K3 surfaces.
A theorem by Orlov states that any equivalence between the bounded derived categories of coherent sheaves of two smooth projective varieties, X and Y, is isomorphic to a Fourier-Mukai transform with kernel in the bounded derived category of…
We study full exact functors between triangulated categories. With some hypotheses on the source category we prove that it admits an orthogonal decomposition into two pieces such that the functor restricted to one of them is zero while the…
We propose some variants of Lefschetz fixed point theorem for Fourier-Mukai functors on a smooth projective algebraic variety. Independently we also suggest a similar theorem for endo-functors on the category of perfect modules over a…
The theory of integral, or Fourier-Mukai, transforms between derived categories of sheaves is a well established tool in noncommutative algebraic geometry. General "representation theorems" identify all reasonable linear functors between…
We prove that the kernels of Fourier-Mukai functors are not unique in general. On the other hand we show that the cohomology sheaves of those kernels are unique. We also discuss several properties of the functor sending an object in the…
Let $X$, $Y$ be smooth projective varieties over $\mathbf{C}$. Let $K$ be a bounded complex of coherent sheaves on $X\times Y$ and let $\Phi_K \colon \mathsf{D}^b_{\mathsf{Coh}}(X) \to \mathsf{D}^b_{\mathsf{Coh}}(Y)$ be the resulting…
We show that Bondal-Orlov's reconstruction theorem holds in noncommutative projective geometry. We also prove that fully faithful exact functors between derived categories of noncommutative projective schemes are of Fourier-Mukai type.
Family Floer theory yields a functor from the Fukaya category of a symplectic manifold admitting a Lagrangian torus fibration to a (twisted) category of perfect complexes on the mirror rigid analytic space. This functor is shown to be…
Given a Fourier-Mukai functor $\Phi$ in the general setting of singular schemes, under various hypotheses we provide both left and a right adjoints to $\Phi$, and also give explicit formulas for them. These formulas are simple and natural,…
We study the Fourier-Mukai functor D(Y) -> D(X) induced by the universal family on a fine moduli space Y for simple semihomogeneous vector bundles on an abelian variety X. The main result is that the Fourier-Mukai transform of a very…