Homological mirror symmetry for projective K3 surfaces

Abstract

We prove the homological mirror symmetry conjecture of Kontsevich for K3 surfaces in the following form: The Fukaya category of a projective K3 surface is equivalent to the derived category of coherent sheaves on the mirror, which is a K3 surface of Picard rank $19$ over the field $\mathbb{C}((q))$ of formal Laurent series. This builds on prior work of Seidel, who proved the theorem in the case of the quartic surface, Sheridan, Lekili--Ueda, and Ganatra--Pardon--Shende.