Sequences of ICE-closed subcategories via preordered τ^-1-rigid modules

2024/10/02 by Hanson, Eric J. · 1 citation
#16E35 #16G10 #16G20 (primary) #18G80 (secondary) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2410.01963

Abstract

Let Λ be a finite-dimensional basic algebra. Sakai recently used certain sequences of image-cokernel-extension-closed (ICE-closed) subcategories of finitely generated Λ-modules to classify certain (generalized) intermediate t-structures in the bounded derived category. We classifying these "contravariantly finite ICE-sequences" using concepts from τ-tilting theory. More precisely, we introduce "cogen-preordered τ^-1-rigid modules" as a generalization of (the dual of) the "TF-ordered τ-rigid modules" of Mendoza and Treffinger. We then establish a bijection between the set of cogen-preordered τ^-1-rigid modules and certain sequences of intervals of torsion-free classes. Combined with the results of Sakai, this yields a bijection with the set of contravariantly finite ICE-sequences (of finite length), and thus also with the set of (m+1)-intermediate t-structures whose aisles are homology-determined.

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• Bricks and τ-tilting theory under base field extensions

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