Abstract
The concept of Koszulity for differential graded (DG, for short) modules is introduced. It is shown that any bounded below DG module with bounded Ext-group to the trivial module over a Koszul DG algebra has a Koszul DG submodule (up to a shift and truncation), moreover such a DG module can be approximated by Koszul DG modules (Theorem 3.6). Let A be a Koszul DG algebra, and D c(A) be the full triangulated subcategory of the derived category of DG A-modules generated by the object A A . If the trivial DG module k A lies in D c(A), then the heart of the standard t-structure on D c(A) is anti-equivalent to the category of finitely generated modules over some finite dimensional algebra. As a corollary, D c(A) is equivalent to the bounded derived category of its heart as triangulated categories.
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This work was supported by National Natural Science Foundation of China (Grant No. 10801099), Doctorate Foundation of Ministry of Education of China (Grant No. 20060246003), and Foundation of Zhejiang Province’s Educational Committee (Grant No. 20070501)
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He, J., Wu, Q. Koszul differential graded modules. Sci. China Ser. A-Math. 52, 2027–2035 (2009). https://doi.org/10.1007/s11425-008-0169-x
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DOI: https://doi.org/10.1007/s11425-008-0169-x