K-flatness in Grothendieck categories: application to quasi-coherent sheaves
- Estrada Domínguez, Sergio 1
- Gillespie, James
- Odabaşi, Sinem 1
-
1
Universidad de Murcia
info
Revista:
Collectanea Mathematica
ISSN: 0010-0757, 2038-4815
Any de publicació: 2024
Tipus: Article
Altres publicacions en: Collectanea Mathematica
Informació de finançament
Finançadors
-
Ministerio de Ciencia e Innovación
- PID2020-113206GB-I00
- PID2020-113206GB-I00
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Fundación Séneca
- 22004/PI/22
- 22004/PI/22
- Universidad de Murcia
Referències bibliogràfiques
- Adamek, J., Rosicky, J.: Locally presentable and accessible categories London Mathematical Society lecture note series, p. 189. Cambridge University Press, Cambridge (1994)
- Bazzoni, S., Cortés-Izurdiaga, M., Estrada, S.: Periodic modules and acyclic complexes. Algebr. Represent. Theory 23(5), 1861–1883 (2020)
- Bühler, T.: Exact Categories. Expo. Math. 28(1), 1–69 (2010)
- Lars Winther Christensen: Sergio Estrada, and Peder Thompson, The stable category of Gorenstein flat sheaves on a Noetherian scheme. Proc. Am. Math. Soc. 149(2), 525–538 (2021)
- Emmanouil, I.: On pure acyclic complexes. J. Algebra 465, 190–213 (2016)
- Emmanouil, I.: On the relation between K-flatness and K-projectivity. J. Algebra 517, 320–335 (2019)
- Emmanouil, I.: K-flatness and orthogonality in homotopy categories. Isr. J. Math. (2022). https://doi.org/10.1007/s11856-022-2413-4
- Emmanouil, Ioannis, Kaperonis, Ilias: On K-absolutely pure complexes, (2022) preprint at https://users.uoa.gr/~emmanoui/research.html
- Estrada, S., Gillespie, J., Odabaşı, S.: Pure exact structures and the pure derived category of a scheme. Math. Proc. Cambridge Philos. Soc. 163(2), 251–264 (2017)
- Estrada, S., Pedro, A., Guil, A., Sinem, O.: Phantom covering ideals in categories without enough projective morphisms. J. Algeb. 562, 94–114 (2020)
- Gillespie, J.: The flat model structure on Ch(R). Trans. Am. Math. Soc. 356(8), 3369–3390 (2004)
- Gillespie, J.: Cotorsion pairs and degreewise homological model structures. Homol. Homot. Appl. 10(1), 283–304 (2008)
- Gillespie, J.: Model structures on exact categories. J. Pure Appl. Algeb. 215(12), 2892–2902 (2011)
- Gillespie, J.: The derived category with respect to a generator. Ann. Mat. Pura Appl. 195(4), 371–402 (2016)
- Gillespie, J.: Gorenstein complexes and recollements from cotorsion pairs. Adv. Math. 291, 859–911 (2016)
- Gillespie, J.: On Ding injective, Ding projective and Ding flat modules and complexes. Rocky Mountain J. Math. 47(8), 2641–2673 (2017)
- Gillespie, J.: K-flat complexes and derived categories. Bull. Lond. Math. Soc. 55(1), 119–136 (2023)
- Gillespie, J.: The homotopy category of acyclic complexes of pure-projective modules. Forum Math. 35(2), 507–521 (2023). https://doi.org/10.1515/forum-2022-0183
- Hartshorne, R., Geometry, A.: Grauate Texts in Mathematics, vol. 52. Springer-Verlag, New York (1977)
- Hovey, M.: Cotorsion pairs, model category structures, and representation theory. Math. Zeitsch. 241, 553–592 (2002)
- Lane, S.M.: Homology, Die Grundlehren der mathematischen Wissenschaften, vol.114, Springer-Verlag, (1963)
- Murfet, D.: The mock homotopy category of projectives and Grothendieck duality, PhD thesis, Australian National University, (2007). (online at https://www.therisingsea.org.)
- Positselski, L., Št’ovíček, J.: Flat quasi-coherent sheaves as direct limits, and quasi-coherent cotorsion periodicity, arXiv:2212.09639v1
- Quillen, D.: Homotopical algebra, SLNM vol. 43, Springer-Verlag, (1967)
- Saorín, M., Št’ovíček, J.: On exact categories and applications to triangulated adjoints and model structures. Adv. Math. 228(2), 968–1007 (2011)
- Št’ovíček, Jan: On purity and applications to coderived and singularity categories, (2014), arXiv: 1412.1615
- Spaltenstein, N.: Resolutions of unbounded complexes. Compos. Math. 65(2), 121–154 (1988)
- Weibel, C.A.: An Introduction to Homological Algebra Cambridge Studies in Advanced Mathematics. Cambridge University Press: Cambridge. pp 38 (1994)