Complete intersection dimension
Publications Mathématiques de l'IHÉS, Volume 86  (1997), p. 67-114
@article{PMIHES_1997__86__67_0,
     author = {Avramov, Luchezar L. and Gasharov, Vesselin N. and Peeva, Irena V.},
     title = {Complete intersection dimension},
     journal = {Publications Math\'ematiques de l'IH\'ES},
     publisher = {Institut des Hautes \'Etudes Scientifiques},
     volume = {86},
     year = {1997},
     pages = {67-114},
     zbl = {0918.13008},
     mrnumber = {99c:13033},
     language = {en},
     url = {http://www.numdam.org/item/PMIHES_1997__86__67_0}
}
Avramov, Luchezar L.; Gasharov, Vesselin N.; Peeva, Irena V. Complete intersection dimension. Publications Mathématiques de l'IHÉS, Volume 86 (1997) , pp. 67-114. http://www.numdam.org/item/PMIHES_1997__86__67_0/

[1] J. Alperin, L. Evens, Representations, resolutions, and Quillen's dimension theorem, J. Pure Appl. Algebra 22 (1981), 1-9. | MR 82j:20020 | Zbl 0469.20008

[2] D. Anick, A counterexample to a conjecture of Serre, Ann. of Math. 115 (1982), 1-33. | MR 86i:55011a | Zbl 0454.55004

[3] M. André, Hopf algebras with divided powers, J. Algebra 18 (1971), 19-50. | MR 43 #3323 | Zbl 0217.07102

[4] E. F. Assmus, Jr., On the homology of local rings, Ill. J. Math. 3 (1959), 187-199. | MR 21 #2670 | Zbl 0085.02401

[5] M. Auslander, M. Bridger, Stable module theory, Mem. Amer. Math. Soc. 94 (1969). | MR 42 #4580 | Zbl 0204.36402

[6] L. L. Avramov, Obstructions to the existence of multiplicative structures on minimal free resolutions, Amer. J. Math. 103 (1981), 1-31. | MR 82m:13011 | Zbl 0447.13006

[7] L. L. Avramov, Local algebra and rational homotopy, Homotopie algébrique et algèbre locale (J.-M. LEMAIRE, J.-C. THOMAS, eds.), Astérisque, vol. 113-114, Soc. Math. France, Paris, 1984, p. 15-43. | Zbl 0552.13003

[8] L. L. Avramov, Modules of finite virtual projective dimension, Invent. math. 96 (1989), 71-101. | MR 90g:13027 | Zbl 0677.13004

[9] L. L. Avramov, Homological asymptotics of modules over local rings, Commutative algebra (M. HOCHSTER, C. HUNEKE, J. SALLY, eds.), MSRI Publ., vol. 15, Springer, New York, 1989, p. 33-62. | MR 90i:13014 | Zbl 0788.18010

[10] L. L. Avramov, Local rings over which all modules have rational Poincaré series, J. Pure Appl. Algebra 91 (1994), 29-48. | MR 94m:13019 | Zbl 0794.13010

[11] L. L. Avramov, A. R. Kustin, M. Miller, Poincaré series of modules over local rings of small embedding codepth or small linking number, J. Algebra 118 (1988), 162-204. | MR 89k:13013 | Zbl 0648.13008

[12] L. L. Avramov, L.-C. Sun, Cohomology operators defined by a deformation, J. Algebra, to appear. | Zbl 0915.13009

[13] D. J. Benson, J. F. Carlson, Projective resolutions and Poincaré duality complexes, Trans. Amer. Math. Soc. 342 (1994), 447-488. | MR 94f:20100 | Zbl 0816.20044

[14] N. Bourbaki, Algèbre. III, Nouvelle édition, Paris, Hermann, 1970.

[15] N. Bourbaki, Algèbre commutative. IX, Paris, Masson, 1983.

[16] R.-O. Buchweitz, G.-M. Greuel, F. Schreyer, Cohen-Macaulay modules on hypersurface singularities. II, Invent. math. 88 (1987), 165-182. | MR 88d:14005 | Zbl 0617.14034

[17] J. A. Eagon, M. Hochster, R-sequences and indeterminates, Quart. J. Math. Oxford Ser. (2) 25 (1974), 61-71. | MR 49 #2703 | Zbl 0278.13008

[18] D. Eisenbud, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc. 260 (1980), 35-64. | MR 82d:13013 | Zbl 0444.13006

[19] D. Eisenbud, S. Goto, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), 89-133. | MR 85f:13023 | Zbl 0531.13015

[20] Y. Félix, S. Halperin, C. Jacobsson, C. Löfwall, J.-C. Thomas, The radical of the homotopy Lie algebra, Amer. J. Math., 110 (1988), 301-322. | MR 89d:55029 | Zbl 0654.55011

[21] V. N. Gasharov, I. V. Peeva, Boundedness versus periodicity over commutative local rings, Trans. Amer. Math. Soc. 320 (1990), 569-580. | MR 90k:13011 | Zbl 0706.13020

[22] A. Grothendieck, Éléments de géométrie algébrique. IV2, Publ. Math. IHES 24 (1965). | Numdam | Zbl 0135.39701

[23] T. H. Gulliksen, A change of rings theorem, with applications to Poincaré series and intersection multiplicity, Math. Scand. 34 (1974), 167-183. | MR 51 #487 | Zbl 0292.13009

[24] T. H. Gulliksen, On the deviations of a local ring, Math. Scand. 47 (1980), 5-20. | MR 82c:13022 | Zbl 0458.13010

[25] J. Herzog, B. Ulrich, J. Backelin, Linear maximal Cohen-Macaulay modules over strict complete intersections, J. Pure Appl. Algebra 71 (1991), 187-202. | MR 92g:13011 | Zbl 0734.13007

[26] A. R. Kustin, S. M. Palmer, The Poincaré series of every finitely generated module over a codimension 4 almost complete intersection is a rational function, J. Pure Appl. Algebra 95 (1994), 271-295. | MR 95h:13016 | Zbl 0812.13011

[27] S. Maclane, Homology, Grundlehren Math. Wiss., vol. 114, Springer, Berlin, 1963. | MR 28 #122 | Zbl 0133.26502

[28] Yu. I. Manin, Some remarks on Koszul algebras and quantum groups, Ann. Inst. Fourier (Grenoble) 37 (1987), 191-205. | Numdam | MR 89e:16022 | Zbl 0625.58040

[29] H. Matsumura, Commutative ring theory, Stud. Adv. Math., vol. 8, Cambridge, Univ. Press, 1986. | MR 88h:13001 | Zbl 0603.13001

[30] V. B. Mehta, Endomorphisms of complexes and modules over Golod rings, Ph. D. Thesis, Univ. of California, Berkeley, 1976.

[31] J. W. Milnor, J. C. Moore, On the structure of Hopf algebras, Ann. of Math. (2) 81 (1965), 211-264. | MR 30 #4259 | Zbl 0163.28202

[32] M. Nagata, Local rings, New York, Wiley, 1962. | MR 27 #5790 | Zbl 0123.03402

[33] J. Shamash, The Poincaré series of a local rings, J. Algebra 12 (1969), 453-470. | MR 39 #2751 | Zbl 0189.04004

[34] G. Sjödin, Hopf algebras and derivations, J. Algebra 64 (1980), 218-229. | MR 84a:16016 | Zbl 0429.16008

[35] L.-C. Sun, Growth of Betti numbers over local rings of small embedding codepth or small linking number, J. Pure Appl. Algebra 96 (1994), 57-71. | MR 95j:13014 | Zbl 0836.13008

[36] J. Tate, Homology of Noetherian rings and of local rings, Ill. J. Math. 1 (1957), 14-27. | MR 19,119b | Zbl 0079.05501