Relative derived equivalences and relative homological dimensions |
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Authors: | Sheng Yong Pan |
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Affiliation: | Department of Mathematics, Beijing Jiaotong University, Beijing 100044, P. R. China and Beijing Center for Mathematics and Information Interdisciplinary Sciences, Beijing 100048, P. R. China |
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Abstract: | Let A be a small abelian category. For a closed subbifunctor F of ExtA1(-,-), Buan has generalized the construction of Verdier's quotient category to get a relative derived category, where he localized with respect to F-acyclic complexes. In this paper, the homological properties of relative derived categories are discussed, and the relation with derived categories is given. For Artin algebras, using relative derived categories, we give a relative version on derived equivalences induced by F-tilting complexes. We discuss the relationships between relative homological dimensions and relative derived equivalences. |
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Keywords: | Relative derived category F-tilting complex relative derived equivalence relative homological dimension |
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