Answer
**Answer**: Tendai, a prominent Japanese Buddhist school, was the institution that Dōgen ended his association with. Dōgen, renowned as the founder of the Sōtō school of Zen Buddhism, made the decision to sever ties with Tendai due to ideological differences. Tendai, characterized by its eclectic approach and incorporation of various Buddhist teachings, diverged from Dōgen's vision of a more direct and experiential path to enlightenment found in Zen.