Fourier-Mukai Transform

An integral functor between bounded derived categories of coherent sheaves on algebraic varieties defined by an object (the kernel) on the product, which frequently yields equivalences and transports geometric information through derived categories.

An integral transform between bounded derived categories of coherent sheaves D^b(X) → D^b(Y) determined by an object (the kernel) P in D^b(X×Y); it sends F ∈ D^b(X) to Rπ_{Y*}(π_X^*F ⊗^L P) and encodes correspondences between X and Y at the derived level.