Telescope conjecture for t-structures over noetherian path algebras

2025/05/27 by Enrico Sabatini, Sabatini, Enrico · 2 citations
Mathematics · #16G20 #18G80 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Primary: 16E35 #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Secondary: 16G30

paper · pdf · doi:10.48550/arxiv.2505.20803

openalex publication_date 2025/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let RQ be the path algebra of a Dynkin quiver Q over a commutative noetherian ring R. We show that any homotopically smashing t-structure in the derived category of RQ is compactly generated. We also give a complete description of the compactly generated t-structures in terms of poset homomorphisms from the prime spectrum of the ring Spec(R) to the poset of filtrations of noncrossing partitions of the quiver Filt(Nc(Q)). In the case that R is regular, we also get a complete description of the wide subcategories of the category mod(RQ).

Citations

• Classifying t-structures via ICE-closed subcategories and a lattice of torsion classes
• Wide coreflective subcategories and torsion pairs
• Rigid integral representations of quivers over arbitrary commutative rings
• Tilting complexes and codimension functions over commutative noetherian rings
• Classifying subcategories of modules over Noetherian algebras
• Parametrizing torsion pairs in derived categories
• Definable coaisles over rings of weak global dimension at most one
• Compactly generated t-structures in the derived category of a\n commutative ring
• Derived categories of absolutely flat rings
• t-structures for hereditary categories
• Support theory via actions of tensor triangulated categories
• The Bousfield lattice for truncated polynomial algebras
• Injective representations of infinite quivers. Applications
• Construction of t-structures and equivalences of derived categories

Cited by

• The Balmer spectrum and tensor telescope conjecture for noetherian path algebras
• Telescope conjecture for quiver representations over artinian rings

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• Telescope conjecture for quiver representations over artinian rings
• The Balmer spectrum and tensor telescope conjecture for noetherian path algebras
• Gluing compactly generated t-structures over stalks of affine schemes
• Compactly generated t-structures in the derived category of a\n commutative ring
• Compactly generated tensor t-structures on the derived category of a Noetherian scheme