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. Soc.,
Providence, RI, 2018, pp. 1–23. DOI: 10.1090/conm/716/14424.
L. Angeleri Hügel, Silting objects, Bull. Lond. Math. Soc. 51(4) (2019),
658–690. DOI: 10.1112/blms.12264.
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/
rnw147.
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.
08.035.
I. Assem and N. Marmaridis, Tilting modules over split-by-nilpotent extensions,
Comm. Algebra 26(5) (1998), 1547–1555. DOI: 10.1080/00927879808826
219.
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: 10.
1515/CRELLE.2011.180.
N. Bourbaki, “Elements of Mathematics. Algebra, Part I: Chapters 1–3”,
Translated from the French. Hermann, Paris; Addison-Wesley Publishing Co.,
Reading Mass., 1974.
S. Breaz and G. C. Modoi, Equivalences induced by infinitely generated
silting modules, Algebr. Represent. Theory (2019). DOI: 10.1007/s10468-019-
09930-3.
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/
s10468-015-9569-0
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. Math. Soc.
142(9) (2014), 2973–2981. DOI: 10.1090/S0002-9939-2014-12056-9.
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. Math.
Soc., Zürich, 2008, pp. 393–412. DOI: 10.4171/060-1/12
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. Belg. Sér. A
40(2) (1988), 239–253.
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
Press, Cambridge, 1987. DOI: 10.1017/CBO9781139171762
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.
[26] M. Prest, “Purity, Spectra and Localisation”, Encyclopedia of Mathematics and
its Applications 121, Cambridge University Press, Cambridge, 2009. DOI: 10.
1017/CBO9781139644242
M. Raynaud and L. Gruson, Critères de platitude et de projectivité. Techniques
de «platification» d’un module, Invent. Math. 13 (1971), 1–89. DOI: 10.
1007/BF01390094
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, Algebra,
Logic and Applications 3, Gordon and Breach Science Publishers, Philadelphia,
PA, 1991.
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
