2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/126948The aim of this paper is twofold: First we give an explicit construction of the infinitesimal deformations of the category Coh(X) of coherent sheaves on a smooth projective variety X. Secondly we show that any Fourier-Mukai transform $/Phi/colon D^b(X)/to D^b(Y)$ extends to an equivalence between the derived categories of the deformed Abelian categories.To appear in Journal of Differential GeometryAlgebraic Geometry18E30 14A22 14B10 14E30text