Non-archimedean Gromov-Witten invariants

Abstract

Motivated by mirror symmetry and the enumeration of holomorphic disks, we construct the theory of Gromov-Witten invariants in the setting of non-archimedean analytic geometry. We build on our previous works on derived non-archimedean geometry and non-archimedean quantum K-invariants, as well as recent developments of rigid analytic motives and virtual fundamental classes in derived geometry. Our approach gives also a new perspective for the classical algebraic case.