Classification and nonexistence for t-structures on derived categories of schemes

2024/04/12 by Clark, Alexander, Lank, Pat, Manali-Rahul, Kabeer +1
Mathematics · Physics and Astronomy · #13D09 #13F40 #14F08 (primary) #18G80 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2404.08578

openalex publication_date 2024/04/12 · openalex created_date 2024/04/16 · openalex updated_date 2026/07/28

Abstract

Given a suitable Noetherian scheme, we classify tensor t-structures on the bounded derived category of coherent sheaves and its variants with prescribed support. Furthermore, we show that the existence of such t-structures restricting to perfect complexes detects regularity, recovering a theorem of Neeman in the affine case by different methods. Our tools establish local-to-global principles for tensor t-structures.

Related

• Nonexistence of singly compactly generated t-structures for schemes
• Constant families of t-structures on derived categories of coherent sheaves
• Construction of t-structures and equivalences of derived categories
• Perfectly generated t-structures for algebraic stacks
• The Pure derived category of quasi-coherent sheaves