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The ascent-descent property for 2-termsilting complexes

  • Autores: Simion Breaz
  • Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 64, Nº 2, 2020, págs. 543-562
  • Idioma: inglés
  • DOI: 10.5565/publmat6422007
  • Enlaces
  • Resumen
    • We will prove that over commutative rings the silting property of 2-termcomplexes induced by morphisms between projective modules is preserved and reflectedby faithfully flat extensions.

  • Referencias bibliográficas
    • T. Adachi, O. Iyama, and I. Reiten, _-tilting theory, Compos. Math. 150(3) (2014), 415–452. DOI: 10.1112/S0010437X13007422.
    • L. Angeleri Hügel, On the abundance of silting modules, in: “Surveys in Representation Theory of Algebras”, Contemp. Math. 716, Amer. Math....
    • L. Angeleri Hügel and M. Hrbek, Silting modules over commutative rings, Int. Math. Res. Not. IMRN 2017(13) (2017), 4131–4151. DOI: 10.1093/imrn/...
    • L. Angeleri Hügel, F. Marks, and J. Vitória, Silting modules, Int. Math. Res. Not. IMRN 2016(4) (2016), 1251–1284. DOI: 10.1093/imrn/rnv191.
    • L. Angeleri Hügel, F. Marks, and J. Vitória, Silting modules and ring epimorphisms, Adv. Math. 303 (2016), 1044–1076. DOI: 10.1016/j.aim.2016....
    • I. Assem and N. Marmaridis, Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26(5) (1998), 1547–1555. DOI: 10.1080/00927879808826...
    • S. Bazzoni, I. Herzog, P Príhoda, J. Šaroch, and J. Trlifaj, Pure projective tilting modules, Preprint (2017). arXiv:1703.04745.
    • D. J. Benson, S. B. Iyengar, and H. Krause, Colocalizing subcategories and cosupport, J. Reine Angew. Math. 2012(673) (2012), 161–207. DOI:...
    • N. Bourbaki, “Elements of Mathematics. Algebra, Part I: Chapters 1–3”, Translated from the French. Hermann, Paris; Addison-Wesley Publishing...
    • S. Breaz and G. C. Modoi, Equivalences induced by infinitely generated silting modules, Algebr. Represent. Theory (2019). DOI: 10.1007/s10468-019-...
    • S. Breaz and F. Pop, Cosilting modules, Algebr. Represent. Theory 20(5) (2017), 1305–1321. DOI: 10.1007/s10468-017-9688-x
    • S. Breaz and J. Žemlicka, The defect functor of a homomorphism and direct unions, Algebr. Represent. Theory 19(1) (2016), 181–208. DOI: 10.1007/...
    • S. Breaz and J. Žemlicka, Torsion classes generated by silting modules, Ark. Mat. 56(1) (2018), 15–32. DOI: 10.4310/ARKIV.2018.v56.n1.a2
    • H. Derksen and J. Fei, General presentations of algebras, Adv. Math. 278 (2015), 210–237. DOI: 10.1016/j.aim.2015.03.012
    • S. Estrada, P. Guil Asensio, and J. Trlifaj, Descent of restricted flat Mittag-Leffler modules and generalized vector bundles, Proc. Amer....
    • L. Fuchs, “Infinite Abelian Groups”, Vol. I, Pure and Applied Mathematics 36, Academic Press, New York-London, 1970.
    • G. Garkusha and M. Prest, Torsion classes of finite type and spectra, in: “K-Theory and Noncommutative Geometry”, EMS Ser. Congr. Rep., Eur....
    • M. Hrbek, J. Štovícek, and J. Trlifaj, Zariski locality of quasi-coherent sheaves associated with tilting, Indiana Univ. Math. J. (to appear).
    • G. Jasso, Reduction of _-tilting modules and torsion pairs, Int. Math. Res. Not. IMRN 2015(16) (2015), 7190–7237. DOI: 10.1093/imrn/rnu163
    • B. Keller and D. Vossieck, Aisles in derived categories, Deuxième Contact Franco-Belge en Algèbre (Faulx-les-Tombes, 1987), Bull. Soc. Math....
    • F. Marks and J. Štovícek, Universal localizations via silting, Proc. Roy. Soc. Edinburgh Sect. A 149(2) (2019), 511–532. DOI: 10.1017/prm.2018.37
    • H. Matsumura, “Commutative Ring Theory”, Translated from the Japanese by M. Reid, Cambridge Studies in Advanced Mathematics 8, Cambridge University...
    • J.-i. Miyachi, Extensions of rings and tilting complexes, J. Pure Appl. Algebra 105(2) (1995), 183–194. DOI: 10.1016/0022-4049(94)00145-6
    • A. Neeman, The chromatic tower for D(R), With an appendix by Marcel Bökstedt, Topology 31(3) (1992), 519–532. DOI: 10.1016/0040-9383(92)90047-L....
    • M. Raynaud and L. Gruson, Critères de platitude et de projectivité. Techniques de «platification» d’un module, Invent. Math. 13 (1971), 1–89....
    • J. Rickard, Derived equivalences as derived functors, J. London Math. Soc. (2) 43(1) (1991), 37–48. DOI: 10.1112/jlms/s2-43.1.37
    • L. Silver, Noncommutative localizations and applications, J. Algebra 7(1) (1967), 44–76. DOI: 10.1016/0021-8693(67)90067-1
    • The Stacks project authors, The Stacks project, https://stacks.math. columbia.edu/tag/04VM
    • J. Wei, Semi-tilting complexes, Israel J. Math. 194(2) (2013), 871–893. DOI: 10.1007/s11856-012-0093-1
    • R. Wisbauer, “Foundations of Module and Ring Theory”, A handbook for study and research, Revised and translated from the 1988 German edition,...
    • P. Zhang and J. Wei, Cosilting complexes and AIR-cotilting modules, J. Algebra 491 (2017), 1–31. DOI: 10.1016/j.jalgebra.2017.07.022

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