Remarks on derived complete modules and complexes

0569849 - MÚ 2024 RIV DE eng J - Journal Article
Positselski, Leonid
Remarks on derived complete modules and complexes.
Mathematische Nachrichten. Roč. 296, č. 2 (2023), s. 811-839. ISSN 0025-584X. E-ISSN 1522-2616
R&D Projects: GA ČR(CZ) GA20-13778S
Institutional support: RVO:67985840
Keywords : torsion modules * contramodules * derived categories
OECD category: Pure mathematics
Impact factor: 1, year: 2022
Method of publishing: Limited access
https://doi.org/10.1002/mana.202000140

Let R be a commutative ring and I a finitely generated ideal in R. 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.
Permanent Link: https://hdl.handle.net/11104/0341185