Derived Equivalence induced by n-tilting modules

2009/05/22 by S. Bazzoni, Bazzoni, S., F. Mantese +3
Mathematics · #16E05 #16E30 #FOS: Mathematics #K-Theory and Homology (math.KT) #Rings and Algebras (math.RA) #math.KT #math.RA #msc:16E05 #msc:16E30

paper · pdf · doi:10.48550/arxiv.0905.3696

arxiv created 2009/05/22 · arxiv updated 2009/12/01

Abstract

Let T_R be a right n-tilting module over an arbitrary associative ring R. In this paper we prove that there exists a n-tilting module T'_R equivalent to T_R which induces a derived equivalence between the unbounded derived category \D(R) and a triangulated subcategory \mathcal E_⊥ of \D(\End(T')) equivalent to the quotient category of \D(\End(T')) modulo the kernel of the total left derived functor -⊗^{\mathbb L}_S'T'. In case T_R is a classical n-tilting module, we get again the Cline-Parshall-Scott and Happel's results.

Related

• Symmetric subcategories, tilting modules and derived recollements
• Ringel modules and homological subcategories
• Tilting in Q-shaped derived categories
• Topological endomorphism rings of tilting complexes
• Stratifications of derived categories from tilting modules over tame hereditary algebras