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Derived functors of inverse limits revisited
Stockholm University, Faculty of Science, Department of Mathematics. Stockholm University, Faculty of Science, Department of Mathematics. Matematik.
2006 (English)In: Journal of the London Mathematical Society, ISSN Online ISSN 1469-7750 - Print ISSN 0024-6107, Vol. 73, no 1, 31-47 p.Article in journal (Refereed) Published
Abstract [en]

We prove, correct and extend several results of an earlier paper of ours (using and recalling several of our later papers) about the derived functors of projective limit in abelian categories. In particular we prove that if C is an abelian category satisfying the Grothendieck axioms AB3 and AB4* and having a set of generators then the first derived functor of projective limit vanishes on so-called Mittag-Leffler sequences in C. The recent examples given by Deligne and Neeman show that the condition that the category has a set of generators is necessary. The condition AB4* is also necessary, and indeed we give for each integer $m \geq 1$ an example of a Grothendieck category Cm and a Mittag-Leffler sequence in Cm for which the derived functors of its projective limit vanish in all positive degrees except m. This leads to a systematic study of derived functors of infinite products in Grothendieck categories. Several explicit examples of the applications of these functors are also studied.

Place, publisher, year, edition, pages
2006. Vol. 73, no 1, 31-47 p.
Keyword [en]
deriverade funktorer, Grothendieck-kategorier, inverst limes
National Category
Mathematics
Identifiers
URN: urn:nbn:se:su:diva-13288DOI: doi:10.1112/S0024610705022416OAI: oai:DiVA.org:su-13288DiVA: diva2:179808
Available from: 2008-03-13 Created: 2008-03-13 Last updated: 2011-01-11Bibliographically approved

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