Indecomposable Cohen-Macaulay modules and irreducible maps
Popescu, Dorin ; Roczen, Marko
Compositio Mathematica, Tome 76 (1990), p. 277-294 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)
Publié le : 1990-01-01
@article{CM_1990__76_1-2_277_0,
     author = {Popescu, Dorin and Roczen, Marko},
     title = {Indecomposable Cohen-Macaulay modules and irreducible maps},
     journal = {Compositio Mathematica},
     volume = {76},
     year = {1990},
     pages = {277-294},
     mrnumber = {1078867},
     zbl = {0715.13010},
     language = {en},
     url = {http://dml.mathdoc.fr/item/CM_1990__76_1-2_277_0}
}

Popescu, Dorin; Roczen, Marko. Indecomposable Cohen-Macaulay modules and irreducible maps. Compositio Mathematica, Tome 76 (1990) pp. 277-294. http://gdmltest.u-ga.fr/item/CM_1990__76_1-2_277_0/

[An] M. André, Localisation de la lissité formelle, Manuscripta Math. 13 (1974) 297-307. | MR 357403 | Zbl 0287.18019

[Ar] M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES 36 (1969) 23-58. | Numdam | MR 268188 | Zbl 0181.48802

[AV] M. Artin and J.L. Verdier, Reflexive modules over rational double points, Math. Ann. 270 (1985) 79-82. | MR 769609 | Zbl 0553.14001

[Au1] M. Auslander, Functors and morphisms determined by objects, Proc. Conf. on Representation Theory, Philadelphia 1976, Marcel Dekker, 1978, 1-244. | MR 480688 | Zbl 0383.16015

[Au2] M. Auslander, Rational singularities and almost split sequences, Trans. Amer. Math. Soc. 293 (1986) 511-531. | MR 816307 | Zbl 0594.20030

[Au3] M. Auslander, Isolated singularities and existence of almost split sequences, Proc. ICRA IV, Lect. Notes in Math. 1178 (1986) 194-241. | MR 842486 | Zbl 0633.13007

[AR] M. Auslander and I. Reiten, Almost split sequences for rational double points, Trans. Amer. Math. Soc. 302 (1987) 87-97. | MR 887498 | Zbl 0617.13018

[Ba] L. Badescu, Applications of the Grothendieck duality theory to the study of normal isolated singularities, Rev. Roum. Math. Pures Appl. 24 (1979), 673-689. | MR 546391 | Zbl 0415.14007

[BNP] S. Basarab, V. Nica and D. Popescu, Approximation properties and existential completeness for ring morphisms, Manuscripta Math. 33 (1981) 227-282. | MR 612613 | Zbl 0472.13013

[BR1] A. Brezuleanu and N. Radu, Sur la localisation de la lissité formelle, C.R. Acad. Sci. Paris 276 (1973) 439-441. | MR 318142 | Zbl 0249.13008

[BR2] A. Brezuleanu and N. Radu, Excellent rings and good separation of the module of differentials, Rev. Roum. Math. Pures Appl. 23 (1978) 1455-1470. | MR 530677 | Zbl 0415.13014

[BEH] R.-O. Buchweitz, D. Eisenbud and J. Herzog: Cohen-Macaulay modules on quadrics, in Proceedings, Lambrecht 1985, Lect. Notes in Math. 1273 (1987) 58-116. | MR 915169 | Zbl 0633.13008

[BGS] R.-O. Buchweitz, G.-M. Greuel and F.-O. Schreyer: Cohen-Macaulay modules on hypersurface singularities II, Invent. math. 88 (1987) 165-183. | MR 877011 | Zbl 0617.14034

[Di] E. Dieterich: Reduction of isolated singularities: Comment. Math. Helvetici 62 (1987) 654-676. | MR 920064 | Zbl 0654.14002

[E1] R. Elkik: Solutions d'equations á coefficients dans un anneau hensélien, Ann. Sci. Ecole Norm. Sup. 4e serie 6 (1973) 533-604. | Numdam | MR 345966 | Zbl 0327.14001

[EK] H. Esnault and H. Knörrer: Reflexive modules over rational double points, Math. Ann. 272 (1985) 545-548. | MR 807289 | Zbl 0577.14023

[GK] G.M. Greuel and H. Kröning: Simple singularities in positive characteristic, Preprint, Bonn, Max-Planck Institut für Math. 19 (1988). | MR 1033443

[EGA] A. Grothendieck and J. Diendonne, Elements de geometrie algebrique, Publ. Math. IHES (1964). | Numdam

[He] J. Herzog: Ringe mit nur endlich vielen Isomorphieklassen von maximalen, unzerlegbaren Cohen-Macaulay Moduln, Math. Ann. 233 (1978) 21-34. | MR 463155 | Zbl 0358.13009

[HPR] D. Happel, U. Preiser and C.M. Ringel, Vinberg's characterization of Dynkin diagrams using subadditive functions with application to DTr-periodic modules, Proceedings of the third international conference on representations of algebras, Carleton University, Ottawa 1979, Springer Lecture Notes in Mathematics 832, 280-294. | MR 607159 | Zbl 0446.16032

[Kn] H. Knörrer, Cohen Macaulay modules on hypersurface singularities I, Invent. Math. 88 (1987) 153-165. | MR 877010 | Zbl 0617.14033

[Li] J. Lipman, Rational singularities with applications to algebraic surfaces and unique factorization, Publ. Math. IHES 36 (1969) 195-297. | Numdam | MR 276239 | Zbl 0181.48903

[Ma1] H. Matsumura, Commutative Algebra, Benjamin, New York, 1970. | MR 266911 | Zbl 0211.06501

[Ma2] H. Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1986. | MR 879273 | Zbl 0603.13001

[NP] V. Nica and D. Popescu, A structure theorem on formally smooth morphisms in positive characteristic, J. of Algebra 100 (1986) 436-455. | MR 840587 | Zbl 0604.13003

[Po1] D. Popescu, General Néron desingularization and approximation, Nagoya Math. J. 104 (1986) 85-119. | MR 868439 | Zbl 0592.14014

[Po2] D. Popescu, Indecomposable Cohen Macaulay modules and their multiplicities, to appear in Trans. AMS. | MR 979959 | Zbl 0725.13009

[Re] I. Reiten, Finite dimensional algebras and singularities, in Proceedings, Lambrecht 1985, Springer Lecture Notes in Mathematics, 1273 (1987) 35-57. | MR 915168 | Zbl 0639.16017

[Sc] F.-O. Schreyer, Finite and countable CM-representation type, in Proceedings, Lambrecht 1985, Springer Lecture Notes in Mathematics, 1273 (1987) 9-34. | MR 915167 | Zbl 0719.14024

[Yo] Y. Yoshino, Brauer-Thrall type theorem for maximal Cohen-Macaulay modules, J. Math. Soc. Japan 39 (1987) 719-739. | MR 905636 | Zbl 0615.13008