2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224401We prove that the first order deformations of two smooth projective K3 surfaces are derived equivalent under a Fourier--Mukai transform if and only if there exists a special isometry of the total cohomology groups of the surfaces which preserves the Mukai pairing, an infinitesimal weight-2 decomposition and the orientation of a positive 4-dimensional space. This generalizes the derived version of the Torelli Theorem. Along the way we show the compatibility of the actions on Hochschild homology and singular cohomology of any Fourier--Mukai functor.Main paper by E. Macri and P. Stellari. Appendix by S.Mehrotra. 21 pages. Final version to appear in Int. Math. Res. NotAlgebraic Geometrytext