Weight Structures and Simple dg Modules for Positive dg 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, ...

GENERALIZED t-STRUCTURES: t-STRUCTURES FOR SHEAVES OF DG-MODULES OVER A SHEAF OF DG-ALGEBRAS AND DIAGONAL t-STRUCTURES

t-structures, in the abstract, apply to any triangulated category. However, for the most part, they have been studied so far only in the context of sheaves of modules over sites provided with sheaves of rings. In this paper we define and study t-structures for categories of modules over sites provided with sheaves of dgas and E∞-dgas. A close variant, as we show, are the diagonal t-structures t...

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

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...

Homotopy Dg Algebras Induce Homotopy Bv Algebras

Let TA denote the space underlying the tensor algebra of a vector space A. In this short note, we show that if A is a differential graded algebra, then TA is a differential BatalinVilkovisky algebra. Moreover, if A is an A∞ algebra, then TA is a commutative BV∞ algebra. 1. Main Statement Let (A, dA) be a complex over a commutative ring R. Our convention is that dA is of degree +1. The space TA ...