相关论文: Fourier-Mukai functors and perfect complexes on du…

For a noetherian scheme, we introduce its unbounded stable derived category. This leads to a recollement which reflects the passage from the bounded derived category of coherent sheaves to the quotient modulo the subcategory of perfect…

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,…

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…

Building on Olander's work on algebraic spaces, we prove Orlov's representability theorem relating fully faithful functors and Fourier--Mukai transforms between the bounded derived category of coherent sheaves to the case of smooth, proper,…

We introduce new enhancements for the bounded derived category $D^b(Coh(X))$ of coherent sheaves on a suitable scheme $X$ and for its subcategory $Perf(X)$ of perfect complexes. They are used for translating Fourier-Mukai functors to…

The classical Fourier-Mukai duality establishes an equivalence of categories between the derived categories of sheaves on dual complex tori. In this article we show that this equivalence extends to an equivalence between two dual objects.…

In 1996, Rothstein and Laumon simultaneously constructed a Fourier-Mukai transform for D-modules over a locally noetherian base of characteristic 0. This functor induces an equivalence of categories between quasi-coherent sheaves of…

We investigate conditions for a Fourier-Mukai transform between derived categories of coherent sheaves on smooth projective stacks endowed with actions by finite groups to lift to the associated equivariant derived categories. As an…

We prove that a coherent DQ-kernel induces an equivalence between the derived categories of DQ-modules with coherent cohomology if and only if the graded commutative kernel associated to it induces an equivalence between the derived…

For $X$ a smooth quasi-projective variety and $X^{[n]}$ its associated Hilbert scheme of $n$ points, we study two canonical Fourier--Mukai transforms $D(X)\to D(X^{[n]})$, the one along the structure sheaf and the one along the ideal sheaf…

We develop some methods for studying the Fourier-Mukai partners of an algebraic variety. As applications we prove that abelian varieties have finitely many Fourier-Mukai partners and that they are uniquely determined by their derived…

Let $X$ be a smooth projective variety. We study a relationship between the derived category of $X$ and that of a canonical divisor. As an application, we will study Fourier-Mukai transforms when $\kappa (X)=dim X-1$.

We show that the adjunction counits of a Fourier-Mukai transform $\Phi$ from $D(X_1)$ to $D(X_2)$ arise from maps of the kernels of the corresponding Fourier-Mukai transforms. In a very general setting of proper separable schemes of finite…

We construct a version of Fourier transform for families of real tori. This transform defines a functor from certain category associated with a symplectic family of tori to the category of holomorphic vector bundles on the dual family (the…

We consider elliptic fibrations with arbitrary base dimensions, and generalise previous work by the second author. In particular, we check universal closedness for the moduli of semistable objects with respect to a polynomial stability that…

We discuss homological mirror symmetry of Fermat polynomials in terms of derived Morita equivalence between derived categories of coherent sheaves and Fukaya-Seidel categories (a.k.a. perfect derived categories of directed Fukaya…

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.

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,…

The paper sets out a generalized framework for Fourier-Mukai transforms and illustrates their use via vector bundle transforms. A Fourier-Mukai transform is, roughly, an isomorphism of derived categories of (sheaves) on smooth varieties X…

In this paper we prove that a morphism between schemes or stacks naturally corresponds to a symmetric monoidal functor between stable infinity-categories of quasi-coherent complexes. It can be viewed as a derived analogue of Tannaka…