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 Dc(A) be the full triangulated subcategory of the derived category of DG A-modules generated by the object AA. If the trivial DG module kA lies in Dc(A), then the heart of the standard t-structure on Dc(A) is anti-equivalent to the category of finitely generated modules over some finite dimensional algebra. As a corollary, Dc(A) is equivalent to the bounded derived category of its heart as triangulated categories.
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