Paper
On t-structures adjacent and orthogonal to weight structures
Authors
Mikhail V. Bondarko
Abstract
We study -structures (on triangulated categories) that are closely related to weight structures.
A -structure couple is said to be adjacent to a weight structure if .
For a category that satisfies the Brown representability property we prove that that is adjacent to exists if and only if is smashing (that is, "respects C-coproducts"). The heart of this is the category of those functors that respect products (here is the heart of ); the result has important applications.
We prove several more statements on constructing -structures starting from weight structures; we look for a strictly orthogonal -structure on some (where are triangulated subcategories of a common ) such that (resp. ) is characterized by the vanishing of morphisms from (resp. ). Some of these results generalize properties of semi-orthogonal decompositions proved in the previous paper, and can be applied to various derived categories of (quasi)coherent sheaves on a scheme that is projective over an affine noetherian one. We also study hearts of orthogonal -structures and their restrictions, and prove some statements on "reconstructing" weight structures from orthogonal -structures.