English

Extension Groups for DG Modules

Commutative Algebra 2016-04-05 v1

Abstract

Let MM and NN be differential graded (DG) modules over a positively graded commutative DG algebra AA. We show that the Ext-groups ExtAi(M,N)\operatorname{Ext}^i_A(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExtAi(M,N)\operatorname{YExt}^i_A(M,N) 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.

Keywords

Cite

@article{arxiv.1604.00516,
  title  = {Extension Groups for DG Modules},
  author = {Saeed Nasseh and Sean Sather-Wagstaff},
  journal= {arXiv preprint arXiv:1604.00516},
  year   = {2016}
}

Comments

11 pages, separated from arXiv:1201.0037

R2 v1 2026-06-22T13:23:51.411Z