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arXiv · 1806.00883

The (he)art of gluing

Giovanni Luca Marchetti·Domenico Fiorenza
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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.

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Giovanni Luca Marchetti, Domenico Fiorenza. 2018-06-03. The (he)art of gluing. https://arxiv.org/abs/1806.00883

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