Derived Equivalence induced by $n$-tilting modules
Bazzoni, S. ; Mantese, F. ; Tonolo, A.
arXiv, 0905.3696 / Harvested from arXiv
Text on arXiv
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 $\mathcal E_{\perp}$ of $\D(\End(T'))$ equivalent to the quotient category of $\D(\End(T'))$ modulo the kernel of the total left derived functor $-\otimes^{\mathbb L}_{S'}T'$. In case $T_R$ is a classical $n$-tilting module, we get again the Cline-Parshall-Scott and Happel's results.
Publié le : 2009-05-22
Classification:  Mathematics - Rings and Algebras,  Mathematics - K-Theory and Homology,  16E05,  16E30 
@article{0905.3696,
     author = {Bazzoni, S. and Mantese, F. and Tonolo, A.},
     title = {Derived Equivalence induced by $n$-tilting modules},
     journal = {arXiv},
     volume = {2009},
     number = {0},
     year = {2009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0905.3696}
}

Bazzoni, S.; Mantese, F.; Tonolo, A. Derived Equivalence induced by $n$-tilting modules. arXiv, Tome 2009 (2009) no. 0, . http://gdmltest.u-ga.fr/item/0905.3696/