[1]

T. Adachi, O. Iyama and I. Reiten,
τ-tilting theory,
Compos. Math. 150 (2014), no. 3, 415–452.
Web of ScienceCrossrefGoogle Scholar

[2]

T. Aihara and O. Iyama,
Silting mutation in triangulated categories,
J. Lond. Math. Soc. 85 (2012), no. 3, 633–668.
CrossrefGoogle Scholar

[3]

M. Auslander and M. Bridger,
Stable module theory,
Mem. Amer. Math. Soc. 94,
American Mathematical Society, Providence 1969.
Google Scholar

[4]

M. Auslander and O. Goldman,
Maximal orders,
Trans. Amer. Math. Soc. 97 (1960), 1–24.
CrossrefGoogle Scholar

[5]

N. Bourbaki,
Commutative algebra, Chapters 1–7,
Springer, Berlin 1998.
Google Scholar

[6]

R.-O. Buchweitz,
Maximal Cohen–Macaulay modules and Tate-cohomology over Gorenstein rings,
preprint (1986), http://hdl.handle.net/1807/16682.

[7]

I. Burban, O. Iyama, B. Keller and I. Reiten,
Cluster tilting for one-dimensional hypersurface singularities,
Adv. Math. 217 (2008), no. 6, 2443–2484.
CrossrefWeb of ScienceGoogle Scholar

[8]

J.-C. Chen,
Flops and equivalences of derived categories for threefolds with only terminal Gorenstein singularities,
J. Differential Geom. 61 (2002), no. 2, 227–261.
CrossrefGoogle Scholar

[9]

H. Dao,
Remarks on non-commutative crepant resolutions of complete intersections,
Adv. Math. 224 (2010), no. 3, 1021–1030.
CrossrefWeb of ScienceGoogle Scholar

[10]

H. Dao and C. Huneke,
Vanishing of Ext, cluster tilting and finite global dimension of endomorphism rings,
Amer. J. Math. 135 (2013), no. 2, 561–578.
CrossrefGoogle Scholar

[11]

D. Eisenbud,
Homological algebra on a complete intersection, with an application to group representations,
Trans. Amer. Math. Soc. 260 (1980), no. 1, 35–64.
CrossrefGoogle Scholar

[12]

D. Happel and L. Unger,
On a partial order of tilting modules,
Algebr. Represent. Theory 8 (2005), no. 2, 147–156.
CrossrefGoogle Scholar

[13]

C. Huneke and R. Wiegand,
Tensor products of modules and the rigidity of Tor,
Math. Ann. 299 (1994), no. 3, 449–476.
CrossrefWeb of ScienceGoogle Scholar

[14]

O. Iyama and I. Reiten,
Fomin–Zelevinsky mutation and tilting modules over Calabi–Yau algebras,
Amer. J. Math. 130 (2008), no. 4, 1087–1149.
CrossrefGoogle Scholar

[15]

O. Iyama and M. Wemyss,
Maximal modifications and Auslander–Reiten duality for non-isolated singularities,
Invent. Math. 197 (2014), no. 3, 521–586.
Web of ScienceCrossrefGoogle Scholar

[16]

O. Iyama and M. Wemyss,
Singular derived categories of $\mathbb{Q}$-factorial terminalizations and maximal modification algebras,
Adv. Math. 261 (2014), 85–121.
Google Scholar

[17]

O. Iyama and Y. Yoshino,
Mutation in triangulated categories and rigid Cohen–Macaulay modules,
Invent. Math. 172 (2008), no. 1, 117–168.
Web of ScienceCrossrefGoogle Scholar

[18]

Y. Liu and B. Zhu,
Triangulated quotient categories,
Comm. Alg. 41 (2013), no. 10, 3720–3738.
CrossrefGoogle Scholar

[19]

A. Nolla de Celis and Y. Sekiya,
Flops and mutations for crepant resolutions of polyhedral singularities,
preprint (2011), http://arxiv.org/abs/1108.2352.

[20]

I. Reiten and M. Van den Bergh,
Two-dimensional tame and maximal orders of finite representation type,
Mem. Amer. Math. Soc. 80 (1989), No. 408.
Google Scholar

[21]

C. Riedtmann and A. Schofield,
On a simplicial complex associated with tilting modules,
Comment. Math. Helv. 66 (1991), no. 1, 70–78.
CrossrefGoogle Scholar

[22]

P. Roberts,
Multiplicities and Chern classes in local algebra,
Cambridge Tracts in Math. 133,
Cambridge University Press, Cambridge 1998.
Google Scholar

[23]

O. Solberg,
Hypersurface singularities of finite Cohen–Macaulay type,
Proc. London Math. Soc. (3) 58 (1989), no. 2, 258–280.
Google Scholar

[24]

M. Van den Bergh,
Three-dimensional flops and noncommutative rings,
Duke Math. J. 122 (2004), no. 3, 423–455.
CrossrefGoogle Scholar

[25]

M. Wemyss,
The $\mathrm{GL}(2,\u2102)$ McKay correspondence,
Math. Ann. 350 (2011), no. 3, 631–659.
Google Scholar

[26]

M. Wemyss,
Aspects of the homological minimal model program,
preprint (2014), http://arxiv.org/abs/1411.7189.

[27]

Y. Yoshino,
Cohen–Macaulay modules over Cohen–Macaulay rings,
London Math. Soc. Lecture Note Ser. 146,
Cambridge University Press, Cambridge 1990.
Google Scholar

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.