Higher nearby cycles and central sheaves on affine flag varieties

In this paper we generalize and study a notion of (unipotent) nearby cycles over a higher dimensional base based on Beĭlinson’s description of unipotent nearby cycles, following an idea of Gaitsgory. This generalization, in the setting of affine Grassmannians, is required in recent work of Bezrukavnikov-Braverman-Finkelberg-Kazhdan.