Construction of t-structures and equivalences of derived categories
By Leovigildo Alonso, A. Jeremias, M. Souto. 2002
117 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/894ed864cd0fa90e7b6d8fc3641d2e06e1cb8bdc
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In Algebra and Number Theory
- Jorge Vit'oria
- Chrysostomos Psaroudakis
- A. Zvonareva
- Pedro Nicolás
- Manuel Saor'in
- Lidia Angeleri Hugel
- J. Št’ovíček
In Geometry and Topology
- Jorge Vit'oria
- Chrysostomos Psaroudakis
- Manuel Saor'in
- A. Zvonareva
- Pedro Nicolás
- J. Št’ovíček
- Lidia Angeleri Hugel
In Mathematical Physics
- Jorge Vit'oria
- Chrysostomos Psaroudakis
- Manuel Saor'in
- A. Zvonareva
- Pedro Nicolás
- J. Št’ovíček
- Lidia Angeleri Hugel
Citations in the corpus
- Silting theory in triangulated categories with coproducts (2015, background): “But the second arrow in this composition is zero since it has domain in U [2] and codomain in U[1].”
- Realisation functors in tilting theory (2015, background): “Since X lies inM⊥>0 , we have thatHomT(M, X [1]) = 0 and, since X [1] lies inM⊥<0 [1] and (τ ≤−1 M M)[1] inM⊥>0 [2], we conclude thatHomT((τ≤−1 M M)[1], X [1]) = 0.”