Derived equivalence induced by infinitely generated $n$-tilting modules
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- by Silvana Bazzoni, Francesca Mantese and Alberto Tonolo
- Proc. Amer. Math. Soc. 139 (2011), 4225-4234
- DOI: https://doi.org/10.1090/S0002-9939-2011-10900-6
- Published electronically: April 28, 2011
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Abstract:
Let $T_R$ be a right $n$-tilting module over an arbitrary associative ring $R$. In this paper we prove that there exists an $n$-tilting module $T’_R$ equivalent to $T_R$ which induces a derived equivalence between the unbounded derived category $\mathcal {D}(R)$ and a triangulated subcategory $\mathcal E_{\perp }$ of $\mathcal {D}(\operatorname {End}(T’))$ equivalent to the quotient category of $\mathcal {D}(\operatorname {End}(T’))$ modulo the kernel of the total left derived functor $-\otimes ^{\mathbb L}_{S’}T’$. If $T_R$ is a classical $n$-tilting module, we have that $T=T’$ and the subcategory $\mathcal E_{\perp }$ coincides with $\mathcal {D}(\operatorname {End}|(T))$, recovering the classical case.References
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Bibliographic Information
- Silvana Bazzoni
- Affiliation: Dipartimento di Matematica Pura ed Applicata, Università di Padova, via Trieste 63, I-35121 Padova, Italy
- MR Author ID: 33015
- Email: bazzoni@math.unipd.it
- Francesca Mantese
- Affiliation: Dipartimento di Informatica, Università degli Studi di Verona, strada Le Grazie 15, I-37134 Verona, Italy
- Email: francesca.mantese@univr.it
- Alberto Tonolo
- Affiliation: Dipartimento di Matematica Pura ed Applicata, Università di Padova, via Trieste 63, I-35121 Padova, Italy
- Email: tonolo@math.unipd.it
- Received by editor(s): February 18, 2010
- Received by editor(s) in revised form: September 9, 2010, and October 21, 2010
- Published electronically: April 28, 2011
- Additional Notes: This research was supported by grant CPDA071244/07 of Padova University and MIUR PRIN 2007
- Communicated by: Harm Derksen
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 4225-4234
- MSC (2010): Primary 16D90, 18E30, 18E35
- DOI: https://doi.org/10.1090/S0002-9939-2011-10900-6
- MathSciNet review: 2823068