Remarks on derived complete modules and complexes

0569849 - MÚ 2024 RIV DE eng J - Článek v odborném periodiku
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
Grant CEP: GA ČR(CZ) GA20-13778S
Institucionální podpora: RVO:67985840
Klíčová slova: torsion modules * contramodules * derived categories
Obor OECD: Pure mathematics
Impakt faktor: 1, rok: 2022
Způsob publikování: Omezený přístup
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.
Trvalý link: https://hdl.handle.net/11104/0341185