Categorial mirror symmetry for K3 surfaces (Q1961076)

The authors show that the constructions given in a previous paper [\textit{C. Bartocci, U. Bruzzo, D. Hernández Ruipérez} and \textit{J. M. Muñoz Porras}, Commun. Math. Phys. 195, No.~1, 79-93 (1998; Zbl 0930.14028)] can be given a categorical interpretation which provides a proof of Kontsevitch's conjecture in the case of K3 surfaces. From the authors' summary: ``Under some assumptions which will be spelled out in the following sections, the derived category of a Fukaya-type category built out of special Lagrangian submanifolds of an elliptic K3 surface X is equivalent to a subcategory of the derived category of coherent sheaves on the mirror surface \(\widehat X\). This subcategory is formed by complexes of sheaves whose zero-th Chern character vanishes''.