The t-structures generated by objects

2018/08/15 by Neeman, Amnon · 4 citations
#Category Theory (math.CT) #FOS: Mathematics #Representation Theory (math.RT) #primary 18E30 #secondary 16G99

paper · doi:10.48550/arxiv.1808.05267

Abstract

Let \mathcal T be a well generated triangulated category, and let S⊂\mathcal T be a set of objects. We prove that there is a t-structure on \mathcal T with \mathcal T^≤0=⟨ S⟩^(-∞,0]. This article is an improvement on the main result of a 2003 article by Alonso, Jeremias and Souto---in that article the theorem was proved under the assumption that \mathcal T has a nice enough model. It should be mentioned that the theorem of Alonso, Jeremias and Souto has been influential---it turns out to be interesting to study all of these t-structures.

Cited by

• Intrinsic homological algebra for triangulated categories
• Nonexistence of singly compactly generated t-structures for schemes
• Telescope conjecture for quiver representations over artinian rings
• Perfectly generated t-structures for algebraic stacks

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