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Statements

Subject Item
n2:RIV%2F00216208%3A11320%2F12%3A10128135%21RIV13-GA0-11320___
rdf:type
skos:Concept n15:Vysledek
rdfs:seeAlso
http://dx.doi.org/10.1016/j.aim.2012.02.013
dcterms: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).
dcterms:title
Almost free modules and Mittag-Leffler conditions Almost free modules and Mittag-Leffler conditions
skos:prefLabel
Almost free modules and Mittag-Leffler conditions Almost free modules and Mittag-Leffler conditions
skos:notation
RIV/00216208:11320/12:10128135!RIV13-GA0-11320___
n15:predkladatel
n16:orjk%3A11320
n3:aktivita
n22:P n22:Z
n3:aktivity
P(GA201/09/0816), Z(MSM0021620839)
n3:cisloPeriodika
6
n3:dodaniDat
n14:2013
n3:domaciTvurceVysledku
n6:6265219
n3:druhVysledku
n21:J
n3:duvernostUdaju
n9:S
n3:entitaPredkladatele
n19:predkladatel
n3:idSjednocenehoVysledku
121712
n3:idVysledku
RIV/00216208:11320/12:10128135
n3:jazykVysledku
n20:eng
n3:klicovaSlova
Quasi-coherent sheaf; Model category structure; Kaplansky class; Deconstructible class; N-1-Projective module; Mittag-Leffler module
n3:klicoveSlovo
n5:N-1-Projective%20module n5:Deconstructible%20class n5:Quasi-coherent%20sheaf n5:Mittag-Leffler%20module n5:Model%20category%20structure n5:Kaplansky%20class
n3:kodStatuVydavatele
US - Spojené státy americké
n3:kontrolniKodProRIV
[F55DF3C0C0C4]
n3:nazevZdroje
Advances in Mathematics
n3:obor
n13:BA
n3:pocetDomacichTvurcuVysledku
1
n3:pocetTvurcuVysledku
2
n3:projekt
n17:GA201%2F09%2F0816
n3:rokUplatneniVysledku
n14:2012
n3:svazekPeriodika
229
n3:tvurceVysledku
Trlifaj, Jan Herbera, Dolors
n3:wos
000301904100010
n3:zamer
n4:MSM0021620839
s:issn
0001-8708
s:numberOfPages
32
n12:doi
10.1016/j.aim.2012.02.013
n7:organizacniJednotka
11320