The (he)art of gluing

Abstract

We introduce a notion of gluability for poset-indexed Bridgeland slicings on triangulated categories and show how a gluing abelian slicing on the heart of a bounded $t$-structure naturally induces a family of perverse $t$-structures. Our setup generalises the one of Collins and Polishchuk. As a corollary we recover several constructions from the theory of $t$-structures on triangulated categories. In particular we rediscover Levine's theorem: the Beilinson-Soul\'e vanishing conjecture implies the existence of Tate motives.