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In this article, we prove that a tame twisted K3 surface over an algebraically closed field of positive characteristic has only finitely many tame twisted Fourier-Mukai partners and we give a counting formula in case we have an ordinary tame untwisted K3 surface. We also show that every tame twisted Fourier Mukai partner of a K3 surface of finite height is a moduli space of twisted sheaves over it.
We prove that a twisted Enriques (respectively, untwisted bielliptic) surface over an algebraically closed field of positive characteristic at least 3 (respectively, at least 5) has no non-trivial Fourier-Mukai partners.
Over complex numbers, the Fourier-Mukai partners of abelian varieties are well-understood. A celebrated result is Orlovs derived Torelli theorem. In this note, we study the FM-partners of abelian varieties in positive characteristic. We notice that,
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 coherent
In this paper we prove that any smooth projective variety of dimension $ge 3$ equipped with a tilting bundle can serve as the source variety of a non-Fourier-Mukai functor between smooth projective schemes.
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 type over a