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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Construction of $t$-structures and equivalences of derived categories


Authors: Leovigildo Alonso Tarrío, Ana Jeremías López and María José Souto Salorio
Journal: Trans. Amer. Math. Soc. 355 (2003), 2523-2543
MSC (2000): Primary 18E30; Secondary 14F05, 16D90
Published electronically: January 30, 2003
MathSciNet review: 1974001
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Abstract: We associate a $t$-structure to a family of objects in $\boldsymbol{\mathsf{D}}(\mathcal{A})$, the derived category of a Grothendieck category $\mathcal{A}$. 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, Be{\u{\i}}\kern.15emlinson's equivalences.


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Additional Information

Leovigildo Alonso Tarrío
Affiliation: Departamento de Álxebra, Facultade de Matemáticas, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
Email: leoalonso@usc.es

Ana Jeremías López
Affiliation: Departamento de Álxebra, Facultade de Matemáticas, Universidade de Santiago de Compostela, E-15782 Santiago de Compostela, Spain
Email: jeremias@usc.es

María José Souto Salorio
Affiliation: Facultade de Informática, Campus de Elviña, Universidade da Coruña, E-15071 A Coruña, Spain
Email: mariaj@udc.es

DOI: http://dx.doi.org/10.1090/S0002-9947-03-03261-6
PII: S 0002-9947(03)03261-6
Received by editor(s): May 14, 2002
Received by editor(s) in revised form: October 30, 2002
Published electronically: January 30, 2003
Additional Notes: The first two authors were partially supported by Spain’s MCyT and E.U.’s FEDER research project BFM2001-3241, supplemented by Xunta de Galicia grant PGDIT 01PX120701PR
Article copyright: © Copyright 2003 American Mathematical Society