. . "000301904100010" . . "11320" . "Quasi-coherent sheaf; Model category structure; Kaplansky class; Deconstructible class; N-1-Projective module; Mittag-Leffler module"@en . "32"^^ . . "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)." . "[F55DF3C0C0C4]" . "Almost free modules and Mittag-Leffler conditions" . "229" . "10.1016/j.aim.2012.02.013" . . . . . "121712" . . "6" . "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 . "Trlifaj, Jan" . . . "Advances in Mathematics" . "P(GA201/09/0816), Z(MSM0021620839)" . "Almost free modules and Mittag-Leffler conditions"@en . "http://dx.doi.org/10.1016/j.aim.2012.02.013" . . "RIV/00216208:11320/12:10128135" . . "0001-8708" . "Almost free modules and Mittag-Leffler conditions" . . "RIV/00216208:11320/12:10128135!RIV13-GA0-11320___" . . . "US - Spojen\u00E9 st\u00E1ty americk\u00E9" . . . "2"^^ . "1"^^ . . "Herbera, Dolors" . . . "Almost free modules and Mittag-Leffler conditions"@en .