ORIGINAL ARTICLE
Remarks on derived complete modules and complexes
Leonid Positselski,
Corresponding Author
Leonid Positselski
Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic
Laboratory of Algebra and Number Theory, Institute for Information Transmission Problems, Moscow, Russia
Correspondence
Leonid Positselski, Institute of Mathematics, Czech Academy of Sciences, Žitná 609/25, 115 67 Prague 1, Czech Republic.
Email: [email protected]
Search for more papers by this authorLeonid Positselski,
Corresponding Author
Leonid Positselski
Institute of Mathematics of the Czech Academy of Sciences, Prague, Czech Republic
Laboratory of Algebra and Number Theory, Institute for Information Transmission Problems, Moscow, Russia
Correspondence
Leonid Positselski, Institute of Mathematics, Czech Academy of Sciences, Žitná 609/25, 115 67 Prague 1, Czech Republic.
Email: [email protected]
Search for more papers by this authorAbstract
Let R be a commutative ring and 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 ones. 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.
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