# Remarks on derived complete modules and complexes

@article{Positselski2020RemarksOD, title={Remarks on derived complete modules and complexes}, author={L. Positselski}, journal={arXiv: Commutative Algebra}, year={2020} }

Let $R$ be a commutative ring and $I\subset R$ a finitely generated ideal. We discuss two definitions of derived $I$-adically complete (also derived $I$-torsion) complexes of $R$-modules which appear in the literature: the idealistic and the sequential one. The two definitions are known to be equivalent for a weakly proregular ideal $I$; we show that they are different otherwise. We argue that the sequential approach works well, but the idealistic one needs to be reinterpreted or properly… Expand

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