Extension Groups for DG Modules

Saeed Nasseh; Sean Sather-Wagstaff

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arXiv · 1604.00516

Extension Groups for DG Modules

Saeed Nasseh·Sean Sather-Wagstaff

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Abstract

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

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Saeed Nasseh, Sean Sather-Wagstaff. 2016-04-02. Extension Groups for DG Modules. https://arxiv.org/abs/1604.00516

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