DG模块的朴素可提升性障碍
Obstruction to naive liftability of DG modules
AI总结：
本文研究了DG代数扩张下DG模块的朴素可提升性障碍，证明其障碍类是特定的上同调类，并给出了满足和不满足该性质的具体DG模例。。
摘要：
DG模块的朴素可提升性概念在[9]和[10]中引入。本文研究DG代数扩张 $A\to B$ 沿的朴素可提升性障碍，其中 $B$ 作为作为底层分级 $A$-模是投射射的。我们证明半自由DG $B$-模 $N$ 的朴素可提升性障碍是 Ext$^1_B(N,N\otimes_B J)$) 中的特定上同调类，其中 $J$ 为对角理想。我们对障碍类的研究结果使我们能够给出满足和不满足朴素提升性质的DG模块的具体例子。
英文摘要：
The notion of naive liftability of DG modules is introduced in [9] and [10]. In this paper, we study the obstruction to naive liftability along extensions $A\to B$ of DG algebras, where $B$ is projective as an underlying graded $A$-module. We show that the obstruction to naive liftability of a semifree DG $B$-module $N$ is a certain cohomology class in Ext$^1_B(N,N\otimes_B J)$, where $J$ is the diagonal ideal. Our results on obstruction class enable us to give concrete examples of DG modules that do and do not satisfy the naive lifting property.
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