Perfectly generated t-structures for algebraic stacks

2025/06/23 by Lank, Pat
#14A30 (primary) #14D23 #14F08 #18G80 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.2506.18803

Abstract

This work studies t-structures for the derived category of quasi-coherent sheaves on a quasi-compact quasi-separated algebraic stack. Specifically, using Thomason filtrations, we classify those t-structures which are generated by perfect complexes and satisfy a tensor compatibility. Interestingly, the only input required is the classification à la Hrbek for the affine scheme case.

Citations

• Perfect generation for regular algebraic stacks
• Nonexistence of singly compactly generated t-structures for schemes
• Compact approximation and descent for algebraic stacks
• Categorical characterizations of regularity for algebraic stacks
• Descending strong generation in algebraic geometry
• Descent and generation for noncommutative coherent algebras over schemes
• Absolute noetherian approximation of algebraic stacks
• Bounded t-structures on the category of perfect complexes over a Noetherian ring of finite Krull dimension
• The t-structures generated by objects
• Compactly generated t-structures in the derived category of a\n commutative ring
• K-theoretic obstructions to bounded t-structures
• One positive and two negative results for derived categories of algebraic stacks
• On some finiteness questions for algebraic stacks
• Quasi-perfect scheme-maps and boundedness of the twisted inverse image\n functor
• The six operations for sheaves on Artin stacks II: Adic Coefficients
• Invariants of t-structures and classification of nullity classes
• The six operations for sheaves on Artin stacks I: Finite Coefficients
• Construction of t-structures and equivalences of derived categories

Related

• Dualizing complexes and t-structures for algebraic stacks
• Compactly generated tensor t-structures on the derived category of a Noetherian scheme
• Classification and nonexistence for t-structures on derived categories of schemes
• Constant families of t-structures on derived categories of coherent sheaves
• Nonexistence of singly compactly generated t-structures for schemes