About: Almost free modules and Mittag-Leffler conditions

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
rdfs:seeAlso	http://dx.doi.org/10.1016/j.aim.2012.02.013
Description	Drinfeld recently suggested to replace projective modules by the flat Mittag-Leffler ones in the definition of an infinite dimensional vector bundle on a scheme X (Drinfeld, 2006 [8]). Two questions arise: (1) What is the structure of the class D of all flat Mittag-Leffler modules over a general ring? (2) Can flat Mittag-Leffler modules be used to build a Quillen model category structure on the category of all chain complexes of quasi-coherent sheaves on X? We answer (1) by showing that a module M is flat Mittag-Leffler, if and only if M is N-1-projective in the sense of Eklof and Mekler (2002) [10]. We use this to characterize the rings such that Disclosed under products, and relate the classes of all Mittag-Leffler, strict Mittag-Leffler, and separable modules. Then we prove that the class D is not deconstructible for any non-right perfect ring. So unlike the classes of all projective and flat modules, the class D does not admit the homotopy theory tools developed recently by Hovey (2002) [26]. This gives a negative answer to (2). Drinfeld recently suggested to replace projective modules by the flat Mittag-Leffler ones in the definition of an infinite dimensional vector bundle on a scheme X (Drinfeld, 2006 [8]). Two questions arise: (1) What is the structure of the class D of all flat Mittag-Leffler modules over a general ring? (2) Can flat Mittag-Leffler modules be used to build a Quillen model category structure on the category of all chain complexes of quasi-coherent sheaves on X? We answer (1) by showing that a module M is flat Mittag-Leffler, if and only if M is N-1-projective in the sense of Eklof and Mekler (2002) [10]. We use this to characterize the rings such that Disclosed under products, and relate the classes of all Mittag-Leffler, strict Mittag-Leffler, and separable modules. Then we prove that the class D is not deconstructible for any non-right perfect ring. So unlike the classes of all projective and flat modules, the class D does not admit the homotopy theory tools developed recently by Hovey (2002) [26]. This gives a negative answer to (2). (en)
Title	Almost free modules and Mittag-Leffler conditions Almost free modules and Mittag-Leffler conditions (en)
skos:prefLabel	Almost free modules and Mittag-Leffler conditions Almost free modules and Mittag-Leffler conditions (en)
skos:notation	RIV/00216208:11320/12:10128135!RIV13-GA0-11320___
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(GA201/09/0816), Z(MSM0021620839)
http://linked.open...iv/cisloPeriodika	6
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Trlifaj, Jan
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Univerzita Karlova v Praze / Matematicko-fyzikální fakulta
http://linked.open...dnocenehoVysledku	121712
http://linked.open...ai/riv/idVysledku	RIV/00216208:11320/12:10128135
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Quasi-coherent sheaf; Model category structure; Kaplansky class; Deconstructible class; N-1-Projective module; Mittag-Leffler module (en)
http://linked.open.../riv/klicoveSlovo	Deconstructible class Kaplansky class Mittag-Leffler module Model category structure N-1-Projective module Quasi-coherent sheaf
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[F55DF3C0C0C4]
http://linked.open...i/riv/nazevZdroje	Advances in Mathematics
http://linked.open...in/vavai/riv/obor	BA
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Algebraické metody teorie reprezentací (aproximace, realizace a omezení)
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	229
http://linked.open...iv/tvurceVysledku	Trlifaj, Jan Herbera, Dolors
http://linked.open...ain/vavai/riv/wos	000301904100010
http://linked.open...n/vavai/riv/zamer	Metody moderní matematiky a jejich aplikace
issn	0001-8708
number of pages	32 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.aim.2012.02.013
http://localhost/t...ganizacniJednotka	11320

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