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Local, colocal, and antilocal properties of modules and complexes over commutative rings
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SYSNO ASEP 0583151 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Local, colocal, and antilocal properties of modules and complexes over commutative rings Tvůrce(i) Positselski, Leonid (MU-W) SAI, ORCID, RID Zdroj.dok. Journal of Algebra. - : Elsevier - ISSN 0021-8693
Roč. 646, 15 May (2024), s. 100-155Poč.str. 56 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova localization ; colocalization ; affine open coverings Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GA20-13778S GA ČR - Grantová agentura ČR Způsob publikování Omezený přístup Institucionální podpora MU-W - RVO:67985840 UT WOS 001194145400001 EID SCOPUS 85185602395 DOI 10.1016/j.jalgebra.2024.02.006 Anotace This paper is a commutative algebra introduction to the homological theory of quasi-coherent sheaves and contraherent cosheaves over quasi-compact semi-separated schemes. Antilocality is an alternative way in which global properties are locally controlled in a finite affine open covering. For example, injectivity of modules over non-Noetherian commutative rings is not preserved by localizations, while homotopy injectivity of complexes of modules is not preserved by localizations even for Noetherian rings. The latter also applies to the contraadjustedness and cotorsion properties. All the mentioned properties of modules or complexes over commutative rings are actually antilocal. They are also colocal, if one presumes contraadjustedness. Generally, if the left class in a (hereditary complete) cotorsion theory for modules or complexes of modules over commutative rings is local and preserved by direct images with respect to affine open immersions, then the right class is antilocal. If the right class in a cotorsion theory for contraadjusted modules or complexes of contraadjusted modules is colocal and preserved by such direct images, then the left class is antilocal. As further examples, the class of flat contraadjusted modules is antilocal, and so are the classes of acyclic, Becker-coacyclic, or Becker-contraacyclic complexes of contraadjusted modules. The same applies to the classes of homotopy flat complexes of flat contraadjusted modules and acyclic complexes of flat contraadjusted modules with flat modules of cocycles. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2025 Elektronická adresa https://doi.org/10.1016/j.jalgebra.2024.02.006
Počet záznamů: 1