Saeed Nasseh

Extension groups for DG modules

ABSTRACT Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups given in terms of equivalence classes of extensions. On the other hand, we show that these groups are isomorphic when the first DG module is semi-projective.

Structure of Irreducible Homomorphisms to/from Free Modules

The primary goal of this paper is to investigate the structure of irreducible monomorphisms to and irreducible epimorphisms from finitely generated free modules over a noetherian local ring. Then we show that over such a ring, self-vanishing of Ext and Tor for a finitely generated module admitting such an irreducible homomorphism forces the ring to be regular.

Geometric aspects of representation theory for DG algebras: answering a question of Vasconcelos

We apply geometric techniques from representation theory to the study of homologically finite differential graded (DG) modules

A Local Ring Has Only Finitely Many Semidualizing Complexes up to Isomorphism

M

Liftings and quasi-liftings of DG modules

over a finite dimensional, positively graded, commutative DG algebra

Local rings with quasi-decomposable maximal ideal

U

Vanishing of Ext and Tor Over Fiber Products

. In particular, in this setting we prove a version of a theorem of Voigt by exhibiting an isomorphism between the Yoneda Ext group

Homology over trivial extensions of commutative DG algebras

operatorname{YExt}^1_U(M,M)

Cohen factorizations: Weak functoriality and applications

and a quotient of tangent spaces coming from an algebraic group action on an algebraic variety. As an application, we answer a question of Vasconcelos from 1974 by showing that a local ring has only finitely many semidualizing complexes up to shift-isomorphism in the derived category

Local rings of embedding codepth at most 3 have only trivial semidualizing complexes

mathcal{D}(R)