Remarks on derived complete modules and complexes
Abstract
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 understood. We also consider $I$adically flat $R$modules.
 Publication:

arXiv eprints
 Pub Date:
 February 2020
 arXiv:
 arXiv:2002.12331
 Bibcode:
 2020arXiv200212331P
 Keywords:

 Mathematics  Commutative Algebra;
 Mathematics  Category Theory
 EPrint:
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