Nonexistence of singly compactly generated t-structures for schemes

2025/11/03 by Bhaduri, Anirban, De Deyn, Timothy, Hrbek, Michal +2
#14A30 (primary) #14D23 #14F08 #18E10 #Algebraic Geometry (math.AG) #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2511.01622

Abstract

We show the first instances of schemes whose standard aisles on their derived category of quasi-coherent sheaves are not singly compactly generated.

Citations

• Compact approximation and descent for algebraic stacks
• Weakly approximable triangulated categories and enhancements: a survey
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• Triangulated categories with a single compact generator and two Brown representability theorems
• Generators versus projective generators in abelian categories
• One positive and two negative results for derived categories of algebraic stacks
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• The six operations for sheaves on Artin stacks I: Finite Coefficients
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Cited by

• Perfectly generated t-structures for algebraic stacks

Related

• Classification and nonexistence for t-structures on derived categories of schemes
• Perfectly generated t-structures for algebraic stacks
• The Pure derived category of quasi-coherent sheaves
• Staggered t-structures on derived categories of equivariant coherent sheaves
• On the stack of 0-dimensional coherent sheaves: structural aspects