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Derived Categories of K3 surfaces and a conjecture of Orlov
Claudio Pedrini (Università di Genova) Let X and Y be smooth complex projective varieties. and let be Db(X) and Db(Y) their derived categories of bounded complexes of coherent sheaves; X and Y are derived equivalent if there is a C-linear equivalence $F : Db(X) ≅ Db(Y). Orlov conjectured that if X and Y are derived equivalent then their motives M(X) and M(Y) are isomorphic in Voevodsky's triangulated category of motives DMgm(C) with Q-coefficients. In a joint paper with Alessio Del Padrone we prove the conjecture in the case X is a K3 surface admitting an elliptic fibration (a case that always occurs if the Picard rank is at least 5) with finite-dimensional Chow motive. We also relate this result with a conjecture by Huybrechts showing that, for a K3 surface with a symplectic involution f, the finite-dimensionality of its motive implies that f, acts as the identity on the Chow group of 0-cycles. |  |
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Organizing committee: Alberto Albano, Elisabetta Ambrogio, Ernesto Buzano, Giuseppe Ceresa, Federica Galluzzi, Marina Marchisio, Claudio Pedrini, Daniela Romagnoli, Alessandro Verra, Giuseppe Vigna Suria