Construction of t-structures and equivalences of derived categories

2002/03/01 by Leovigildo Alonso, Ana Jeremias, Alonso, Leovigildo +4 · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math.AG #math.RT #msc:14F05 #msc:16D90 #msc:18E30

paper · pdf · doi:10.48550/arxiv.math/0203009

Proof of 6.5 clarified, to appear in Trans. A.M.S., 22 pages

arxiv created 2002/10/22 · arxiv updated 2009/11/30

Abstract

We associate a t-structure to a family of objects in D(A), the derived category of a Grothendieck category A. Using general results on t-structures, we give a new proof of Rickard's theorem on equivalence of bounded derived categories of modules. Also, we extend this result to bounded derived categories of quasi-coherent sheaves on separated divisorial schemes obtaining, in particular, Beilinson's equivalences.

Cited by

• The Balmer spectrum and tensor telescope conjecture for noetherian path algebras
• Nonexistence of singly compactly generated t-structures for schemes
• Metric completions of triangulated categories from hereditary rings

Related

• Classification and nonexistence for t-structures on derived categories of schemes
• Constant families of t-structures on derived categories of coherent sheaves
• Bounded t-structures on the bounded derived category of coherent sheaves over a weighted projective line
• Discrete derived categories I: homomorphisms, autoequivalences and\n t-structures
• Self-dual T-structure