Local cohomology and support for triangulated categories

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1. [1] L. Alonso Tarrío, A. Jeremías López & M. J. Souto Salorio, Localization in categories of complexes and unbounded resolutions, Canad. J. Math.52 (2000), 225–247. Zbl0948.18008
2. [2] L. Alonso Tarrío, A. Jeremías López & M. J. Souto Salorio, Bousfield localization on formal schemes, J. Algebra278 (2004), 585–610. Zbl1060.18007
3. [3] L. L. Avramov, Modules of finite virtual projective dimension, Invent. Math.96 (1989), 71–101. Zbl0677.13004MR981738
4. [4] L. L. Avramov, Infinite free resolutions, in Six lectures on commutative algebra (Bellaterra, 1996), Progr. Math. 166, Birkhäuser, 1998, 1–118. Zbl0934.13008MR1648664
5. [5] L. L. Avramov & R.-O. Buchweitz, Homological algebra modulo a regular sequence with special attention to codimension two, J. Algebra230 (2000), 24–67. Zbl1011.13007
6. [6] L. L. Avramov & R.-O. Buchweitz, Support varieties and cohomology over complete intersections, Invent. Math.142 (2000), 285–318. Zbl0999.13008
7. [7] L. L. Avramov, H.-B. Foxby & S. Halperin, Differential graded homological algebra, in preparation. 
8. [8] L. L. Avramov, V. N. Gasharov & I. V. Peeva, Complete intersection dimension, Publ. Math. I.H.É.S. 86 (1997), 67–114. Zbl0918.13008
9. [9] L. L. Avramov & S. B. Iyengar, Constructing modules with prescribed cohomological support, Illinois J. Math.51 (2007), 1–20. Zbl1121.13014
10. [10] L. L. Avramov & L.-C. Sun, Cohomology operators defined by a deformation, J. Algebra204 (1998), 684–710. Zbl0915.13009
11. [11] P. Balmer, Supports and filtrations in algebraic geometry and modular representation theory, Amer. J. Math.129 (2007), 1227–1250. Zbl1130.18005MR2354319
12. [12] A. A. Beĭlinson, J. Bernstein & P. Deligne, Faisceaux pervers, in Analysis and topology on singular spaces, I (Luminy, 1981), Astérisque 100, Soc. Math. France, 1982, 5–171. Zbl0536.14011
13. [13] D. J. Benson, Representations and cohomology. II, Cambridge Studies in Advanced Mathematics 31, Cambridge University Press, 1991. Zbl0731.20001MR1156302
14. [14] D. J. Benson, Commutative algebra in the cohomology of groups, in Trends in commutative algebra, Math. Sci. Res. Inst. Publ. 51, Cambridge Univ. Press, 2004, 1–50. Zbl1113.20042MR2132647
15. [15] D. J. Benson & J. F. Carlson, Varieties and cohomology of infinitely generated modules, Arch. Math. (Basel) 91 (2008), 122–125. Zbl1151.20040
16. [16] D. J. Benson, J. F. Carlson & J. Rickard, Complexity and varieties for infinitely generated modules. II, Math. Proc. Cambridge Philos. Soc. 120 (1996), 597–615. Zbl0888.20003
17. [17] D. J. Benson, S. B. Iyengar & H. Krause, Stratifying modular representations of finite groups, preprint, 2008. Zbl1261.20057
18. [18] D. J. Benson & H. Krause, Pure injectives and the spectrum of the cohomology ring of a finite group, J. reine angew. Math. 542 (2002), 23–51. Zbl0987.20026
19. [19] D. J. Benson & H. Krause, Complexes of injective $kG$-modules, Algebra Number Theory2 (2008), 1–30. Zbl1167.20006
20. [20] P. A. Bergh, On support varieties for modules over complete intersections, Proc. Amer. Math. Soc.135 (2007), 3795–3803. Zbl1127.13008MR2341929
21. [21] W. Bruns & J. Herzog, Cohen-Macaulay rings, Cambridge Studies in Advanced Mathematics 39, Cambridge University Press, 1993. Zbl0788.13005
22. [22] J. F. Carlson, The varieties and the cohomology ring of a module, J. Algebra85 (1983), 104–143. Zbl0526.20040MR723070
23. [23] J. F. Carlson, The variety of an indecomposable module is connected, Invent. Math.77 (1984), 291–299. Zbl0543.20032MR752822
24. [24] H. Cartan & S. Eilenberg, Homological algebra, Princeton University Press, 1956. Zbl0933.18001
25. [25] S. K. Chebolu, Krull-Schmidt decompositions for thick subcategories, J. Pure Appl. Algebra210 (2007), 11–27. Zbl1116.55004MR2311169
26. [26] K. Erdmann, M. Holloway, R. Taillefer, N. Snashall & Ø. Solberg, Support varieties for selfinjective algebras, $K$-Theory 33 (2004), 67–87. Zbl1116.16007
27. [27] H.-B. Foxby, Bounded complexes of flat modules, J. Pure Appl. Algebra15 (1979), 149–172. Zbl0411.13006MR535182
28. [28] H.-B. Foxby & S. B. Iyengar, Depth and amplitude for unbounded complexes, in Commutative algebra (Grenoble / Lyon, 2001), Contemp. Math. 331, Amer. Math. Soc., 2003, 119–137. Zbl1096.13516
29. [29] E. M. Friedlander & J. Pevtsova, $\Pi$-supports for modules for finite group schemes, Duke Math. J.139 (2007), 317–368. Zbl1128.20031
30. [30] P. Gabriel & M. Zisman, Calculus of fractions and homotopy theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 35, Springer New York, Inc., New York, 1967. Zbl0186.56802
31. [31] J. P. C. Greenlees & J. P. May, Derived functors of $I$-adic completion and local homology, J. Algebra149 (1992), 438–453. Zbl0774.18007
32. [32] A. Grothendieck, Cohomologie locale des faisceaux cohérents et théorèmes de Lefschetz locaux et globaux (SGA 2), Documents mathématiques, 4, Soc. Math. France, 2005, Séminaire de Géométrie Algébrique du Bois Marie, 1962. Zbl1079.14001MR2171939
33. [33] T. H. Gulliksen, A change of ring theorem with applications to Poincaré series and intersection multiplicity, Math. Scand.34 (1974), 167–183. Zbl0292.13009MR364232
34. [34] R. Hartshorne, Residues and duality, Lecture notes of a seminar on the work of A. Grothendieck, given at Harvard 1963/64. Lecture Notes in Math., No. 20, Springer, 1966. MR222093
35. [35] M. J. Hopkins, Global methods in homotopy theory, in Homotopy theory (Durham, 1985), London Math. Soc. Lecture Note Ser. 117, Cambridge Univ. Press, 1987, 73–96. Zbl0657.55008MR932260
36. [36] M. Hovey, J. H. Palmieri & N. P. Strickland, Axiomatic stable homotopy theory, Mem. Amer. Math. Soc. 128 (1997), 114. Zbl0881.55001
37. [37] S. B. Iyengar & H. Krause, Acyclicity versus total acyclicity for complexes over Noetherian rings, Doc. Math.11 (2006), 207–240. Zbl1119.13014
38. [38] H. Krause, Decomposing thick subcategories of the stable module category, Math. Ann.313 (1999), 95–108. Zbl0926.20004MR1666825
39. [39] H. Krause, A Brown representability theorem via coherent functors, Topology41 (2002), 853–861. Zbl1009.18010MR1905842
40. [40] H. Krause, The stable derived category of a Noetherian scheme, Compos. Math.141 (2005), 1128–1162. Zbl1090.18006MR2157133
41. [41] H. Krause, Thick subcategories of modules over commutative Noetherian rings, Math. Ann.340 (2008), 733–747. Zbl1143.13012MR2372735
42. [42] L. G. J. Lewis, J. P. May, M. Steinberger & J. E. McClure, Equivariant stable homotopy theory, Lecture Notes in Math. 1213, Springer, 1986. Zbl0611.55001
43. [43] J. Lipman, Lectures on local cohomology and duality, in Local cohomology and its applications (Guanajuato, 1999), Lecture Notes in Pure and Appl. Math. 226, Dekker, 2002, 39–89. Zbl1011.13010MR1888195
44. [44] S. MacLane, Categories for the working mathematician, Graduate Texts in Math. 5, Springer, 1971. Zbl0232.18001MR354798
45. [45] H. R. Margolis, Spectra and the Steenrod algebra, North-Holland Mathematical Library 29, North-Holland Publishing Co., 1983. Zbl0552.55002MR738973
46. [46] H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, 1986. Zbl0603.13001MR879273
47. [47] A. Neeman, The chromatic tower for $D\left(R\right)$, Topology31 (1992), 519–532. Zbl0793.18008MR1174255
48. [48] A. Neeman, Triangulated categories, Annals of Mathematics Studies 148, Princeton University Press, 2001. Zbl0974.18008MR1812507
49. [49] D. Quillen, The spectrum of an equivariant cohomology ring. I, II, Ann. of Math. 94 (1971), 549–572; ibid. 94 (1971), 573–602. Zbl0247.57013MR298694
50. [50] J. Rickard, Idempotent modules in the stable category, J. London Math. Soc.56 (1997), 149–170. Zbl0910.20034MR1462832
51. [51] U. Shukla, Cohomologie des algèbres associatives, Ann. Sci. École Norm. Sup.78 (1961), 163–209. Zbl0228.18005MR132769
52. [52] N. Snashall & Ø. Solberg, Support varieties and Hochschild cohomology rings, Proc. London Math. Soc.88 (2004), 705–732. Zbl1067.16010
53. [53] Ø. Solberg, Support varieties for modules and complexes, in Trends in representation theory of algebras and related topics, Contemp. Math. 406, Amer. Math. Soc., 2006, 239–270. Zbl1115.16007MR2258047
54. [54] R. W. Thomason, The classification of triangulated subcategories, Compositio Math.105 (1997), 1–27. Zbl0873.18003MR1436741

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