Abstract:
This paper studies the derived categories of coherent sheaves on smooth complete algebraic varieties and equivalences between them. We prove that every equivalence of categories is represented by an object on the product of the varieties. This result is applied to describe the Abelian varieties and K3 surfaces that have equivalent derived categories of coherent sheaves.
Federico Caucci, Luigi Lombardi, Giuseppe Pareschi, “Derived invariance of the Albanese relative canonical ring”, Advances in Mathematics, 419 (2023), 108965
Riccardo Moschetti, Marco Rampazzo, “Fullness of the Kuznetsov–Polishchuk Exceptional Collection for the Spinor Tenfold”, Algebr Represent Theor, 2023
Nunez P., “A Note on Semiorthogonal Decompositions For Fano Fibrations”, Geod. Dedic., 216:2 (2022), 20
Kapustka M., Rampazzo M., “Mukai Duality Via Roofs of Projective Bundles”, Bull. London Math. Soc., 54:2 (2022), 694–717
Dmitry Galakhov, “On supersymmetric interface defects, brane parallel transport, order-disorder transition and homological mirror symmetry”, J. High Energ. Phys., 2022:10 (2022)
Srivastava T.K., “Lifting Automorphisms on Abelian Varieties as Derived Autoequivalences”, Arch. Math., 116:5 (2021), 515–527
Husain H.S., Sultana M., “Derived Functor Cohomology Groups With Yoneda Product”, J. Korean Soc. Math. Educ. Ser. B-Pure Appl. Math., 28:2 (2021), 187–198
Neeman A., “Strong Generators in D-Perf(X) and D-Coh(B)(X)”, Ann. Math., 193:3 (2021), 689–732
Marco Rampazzo, Equivalences between Calabi–Yau manifolds and roofs of projective bundles, 2021
Negron C., Schedler T., “the Hochschild Cohomology Ring of a Global Quotient Orbifold”, Adv. Math., 364 (2020), 106978
Achter J.D. Casalaina-Martin S. Vial Ch., “Derived Equivalent Threefolds, Algebraic Representatives, and the Coniveau Filtration”, Math. Proc. Camb. Philos. Soc., 167:1 (2019), 123–131
Markman E., Mehrotra S., Verbitsky M., “Rigid Hyperholomorphic Sheaves Remain Rigid Along Twistor Deformations of the Underlying Hyparkahler Manifold”, Eur. J. Math., 5:3, SI (2019), 964–1012
Krug A., “P-Functor Versions of the Nakajima Operators”, Algebraic Geom., 6:6 (2019), 678–715
Caucci F., Pareschi G., “Derived Invariants Arising From the Albanese Map”, Algebraic Geom., 6:6 (2019), 730–746
Shende V., “the Conormal Torus Is a Complete Knot Invariant”, Forum Math. Pi, 7 (2019), e6
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