紧致DG模和Gorenstein DG代数

DG (co)algebras, DG Lie algebras and L∞ algebras

Weight Structures and Simple Dg Modules for Positive Dg Algebras

Using techniques due to Dwyer–Greenlees–Iyengar we construct weight structures in triangulated categories generated by compact objects. We apply our result to show that, for a dg category whose homology vanishes in negative degrees and is semi-simple in degree 0, each simple module over the homology lifts to a dg module which is unique up to isomorphism in the derived category. This allows us, ...

European Commission Dg Research

Deriving Dg Categories

We investigate the (unbounded) derived category of a diierential Z-graded category (=DG category). As a rst application, we deduce a 'triangulatedanaloguè (4.3) of a theorem of Freyd's 5, Ex. 5.3 H] and Gabriel's 6, Ch. V] characterizing module categories among abelian categories. After adapting some homological algebra we go on to prove a 'Morita theorem`(8.2) generalizing results of 19] and 2...

Duality for Cochain Dg Algebras

This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-commutative aspects. One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology. As an application, it is proved that if the canonical module A/A has a semi-free resolutio...