Extension Groups for DG Modules

2016/04/02 by Nasseh, Saeed, Sather-Wagstaff, Sean
#13D02 #13D07 #13D09 #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.00516

Abstract

Let M and N be differential graded (DG) modules over a positively graded commutative DG algebra A. We show that the Ext-groups Extⁱ_A(M,N) defined in terms of semi-projective resolutions are not in general isomorphic to the Yoneda Ext-groups YExtⁱ_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.

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