Complete intersection dimension
Luchezar L. Avramov; Vesselin N. Gasharov; Irena V. Peeva
Publications Mathématiques de l'IHÉS (1997)
- Volume: 86, page 67-114
- ISSN: 0073-8301
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topAvramov, Luchezar L., Gasharov, Vesselin N., and Peeva, Irena V.. "Complete intersection dimension." Publications Mathématiques de l'IHÉS 86 (1997): 67-114. <http://eudml.org/doc/104126>.
@article{Avramov1997,
author = {Avramov, Luchezar L., Gasharov, Vesselin N., Peeva, Irena V.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {minimal free resolution; Betti numbers; complexity; complete intersection dimension; projective dimension; depth; Tate resolution},
language = {eng},
pages = {67-114},
publisher = {Institut des Hautes Études Scientifiques},
title = {Complete intersection dimension},
url = {http://eudml.org/doc/104126},
volume = {86},
year = {1997},
}
TY - JOUR
AU - Avramov, Luchezar L.
AU - Gasharov, Vesselin N.
AU - Peeva, Irena V.
TI - Complete intersection dimension
JO - Publications Mathématiques de l'IHÉS
PY - 1997
PB - Institut des Hautes Études Scientifiques
VL - 86
SP - 67
EP - 114
LA - eng
KW - minimal free resolution; Betti numbers; complexity; complete intersection dimension; projective dimension; depth; Tate resolution
UR - http://eudml.org/doc/104126
ER -
References
top- [1] J. ALPERIN, L. EVENS, Representations, resolutions, and Quillen's dimension theorem, J. Pure Appl. Algebra 22 (1981), 1-9. Zbl0469.20008MR82j:20020
- [2] D. ANICK, A counterexample to a conjecture of Serre, Ann. of Math. 115 (1982), 1-33. Zbl0454.55004MR86i:55011a
- [3] M. ANDRÉ, Hopf algebras with divided powers, J. Algebra 18 (1971), 19-50. Zbl0217.07102MR43 #3323
- [4] E. F. ASSMUS, Jr., On the homology of local rings, Ill. J. Math. 3 (1959), 187-199. Zbl0085.02401MR21 #2670
- [5] M. AUSLANDER, M. BRIDGER, Stable module theory, Mem. Amer. Math. Soc. 94 (1969). Zbl0204.36402MR42 #4580
- [6] L. L. AVRAMOV, Obstructions to the existence of multiplicative structures on minimal free resolutions, Amer. J. Math. 103 (1981), 1-31. Zbl0447.13006MR82m:13011
- [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. Zbl0552.13003
- [8] L. L. AVRAMOV, Modules of finite virtual projective dimension, Invent. math. 96 (1989), 71-101. Zbl0677.13004MR90g:13027
- [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. Zbl0788.18010MR90i:13014
- [10] L. L. AVRAMOV, Local rings over which all modules have rational Poincaré series, J. Pure Appl. Algebra 91 (1994), 29-48. Zbl0794.13010MR94m:13019
- [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. Zbl0648.13008MR89k:13013
- [12] L. L. AVRAMOV, L.-C. SUN, Cohomology operators defined by a deformation, J. Algebra, to appear. Zbl0915.13009
- [13] D. J. BENSON, J. F. CARLSON, Projective resolutions and Poincaré duality complexes, Trans. Amer. Math. Soc. 342 (1994), 447-488. Zbl0816.20044MR94f:20100
- [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. Zbl0617.14034MR88d:14005
- [17] J. A. EAGON, M. HOCHSTER, R-sequences and indeterminates, Quart. J. Math. Oxford Ser. (2) 25 (1974), 61-71. Zbl0278.13008MR49 #2703
- [18] D. EISENBUD, Homological algebra on a complete intersection, with an application to group representations, Trans. Amer. Math. Soc. 260 (1980), 35-64. Zbl0444.13006MR82d:13013
- [19] D. EISENBUD, S. GOTO, Linear free resolutions and minimal multiplicity, J. Algebra 88 (1984), 89-133. Zbl0531.13015MR85f:13023
- [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. Zbl0654.55011MR89d:55029
- [21] V. N. GASHAROV, I. V. PEEVA, Boundedness versus periodicity over commutative local rings, Trans. Amer. Math. Soc. 320 (1990), 569-580. Zbl0706.13020MR90k:13011
- [22] A. GROTHENDIECK, Éléments de géométrie algébrique. IV2, Publ. Math. IHES 24 (1965). Zbl0135.39701
- [23] T. H. GULLIKSEN, A change of rings theorem, with applications to Poincaré series and intersection multiplicity, Math. Scand. 34 (1974), 167-183. Zbl0292.13009MR51 #487
- [24] T. H. GULLIKSEN, On the deviations of a local ring, Math. Scand. 47 (1980), 5-20. Zbl0458.13010MR82c:13022
- [25] J. HERZOG, B. ULRICH, J. BACKELIN, Linear maximal Cohen-Macaulay modules over strict complete intersections, J. Pure Appl. Algebra 71 (1991), 187-202. Zbl0734.13007MR92g:13011
- [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. Zbl0812.13011MR95h:13016
- [27] S. MACLANE, Homology, Grundlehren Math. Wiss., vol. 114, Springer, Berlin, 1963. Zbl0133.26502MR28 #122
- [28] Yu. I. MANIN, Some remarks on Koszul algebras and quantum groups, Ann. Inst. Fourier (Grenoble) 37 (1987), 191-205. Zbl0625.58040MR89e:16022
- [29] H. MATSUMURA, Commutative ring theory, Stud. Adv. Math., vol. 8, Cambridge, Univ. Press, 1986. Zbl0603.13001MR88h: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. Zbl0163.28202MR30 #4259
- [32] M. NAGATA, Local rings, New York, Wiley, 1962. Zbl0123.03402MR27 #5790
- [33] J. SHAMASH, The Poincaré series of a local rings, J. Algebra 12 (1969), 453-470. Zbl0189.04004MR39 #2751
- [34] G. SJÖDIN, Hopf algebras and derivations, J. Algebra 64 (1980), 218-229. Zbl0429.16008MR84a:16016
- [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. Zbl0836.13008MR95j:13014
- [36] J. TATE, Homology of Noetherian rings and of local rings, Ill. J. Math. 1 (1957), 14-27. Zbl0079.05501MR19,119b
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