Indecomposable Cohen-Macaulay modules and irreducible maps

Dorin Popescu; Marko Roczen

Compositio Mathematica (1990)

  • Volume: 76, Issue: 1-2, page 277-294
  • ISSN: 0010-437X

How to cite

top

Popescu, Dorin, and Roczen, Marko. "Indecomposable Cohen-Macaulay modules and irreducible maps." Compositio Mathematica 76.1-2 (1990): 277-294. <http://eudml.org/doc/90051>.

@article{Popescu1990,
author = {Popescu, Dorin, Roczen, Marko},
journal = {Compositio Mathematica},
keywords = {bound properties on maximal Cohen-Macaulay modules; henselian ring; Auslander-Reiten quivers; Gorenstein isolated singularity},
language = {eng},
number = {1-2},
pages = {277-294},
publisher = {Kluwer Academic Publishers},
title = {Indecomposable Cohen-Macaulay modules and irreducible maps},
url = {http://eudml.org/doc/90051},
volume = {76},
year = {1990},
}

TY - JOUR
AU - Popescu, Dorin
AU - Roczen, Marko
TI - Indecomposable Cohen-Macaulay modules and irreducible maps
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 76
IS - 1-2
SP - 277
EP - 294
LA - eng
KW - bound properties on maximal Cohen-Macaulay modules; henselian ring; Auslander-Reiten quivers; Gorenstein isolated singularity
UR - http://eudml.org/doc/90051
ER -

References

top
  1. [An] M. André, Localisation de la lissité formelle, Manuscripta Math.13 (1974) 297-307. Zbl0287.18019MR357403
  2. [Ar] M. Artin, Algebraic approximation of structures over complete local rings, Publ. Math. IHES36 (1969) 23-58. Zbl0181.48802MR268188
  3. [AV] M. Artin and J.L. Verdier, Reflexive modules over rational double points, Math. Ann.270 (1985) 79-82. Zbl0553.14001MR769609
  4. [Au1] M. Auslander, Functors and morphisms determined by objects, Proc. Conf. on Representation Theory, Philadelphia1976, Marcel Dekker, 1978, 1-244. Zbl0383.16015MR480688
  5. [Au2] M. Auslander, Rational singularities and almost split sequences, Trans. Amer. Math. Soc.293 (1986) 511-531. Zbl0594.20030MR816307
  6. [Au3] M. Auslander, Isolated singularities and existence of almost split sequences, Proc. ICRA IV, Lect. Notes in Math.1178 (1986) 194-241. Zbl0633.13007MR842486
  7. [AR] M. Auslander and I. Reiten, Almost split sequences for rational double points, Trans. Amer. Math. Soc.302 (1987) 87-97. Zbl0617.13018MR887498
  8. [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. Zbl0415.14007MR546391
  9. [BNP] S. Basarab, V. Nica and D. Popescu, Approximation properties and existential completeness for ring morphisms, Manuscripta Math.33 (1981) 227-282. Zbl0472.13013MR612613
  10. [BR1] A. Brezuleanu and N. Radu, Sur la localisation de la lissité formelle, C.R. Acad. Sci. Paris276 (1973) 439-441. Zbl0249.13008MR318142
  11. [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. Zbl0415.13014MR530677
  12. [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. Zbl0633.13008MR915169
  13. [BGS] R.-O. Buchweitz, G.-M. Greuel and F.-O. Schreyer: Cohen-Macaulay modules on hypersurface singularities II, Invent. math.88 (1987) 165-183. Zbl0617.14034MR877011
  14. [Di] E. Dieterich: Reduction of isolated singularities: Comment. Math. Helvetici62 (1987) 654-676. Zbl0654.14002MR920064
  15. [E1] R. Elkik: Solutions d'equations á coefficients dans un anneau hensélien, Ann. Sci. Ecole Norm. Sup.4e serie 6 (1973) 533-604. Zbl0327.14001MR345966
  16. [EK] H. Esnault and H. Knörrer: Reflexive modules over rational double points, Math. Ann.272 (1985) 545-548. Zbl0577.14023MR807289
  17. [GK] G.M. Greuel and H. Kröning: Simple singularities in positive characteristic, Preprint, Bonn, Max-Planck Institut für Math.19 (1988). Zbl0715.14001MR1033443
  18. [EGA] A. Grothendieck and J. Diendonne, Elements de geometrie algebrique, Publ. Math. IHES (1964). 
  19. [He] J. Herzog: Ringe mit nur endlich vielen Isomorphieklassen von maximalen, unzerlegbaren Cohen-Macaulay Moduln, Math. Ann.233 (1978) 21-34. Zbl0358.13009MR463155
  20. [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, Ottawa1979, Springer Lecture Notes in Mathematics832, 280-294. Zbl0446.16032MR607159
  21. [Kn] H. Knörrer, Cohen Macaulay modules on hypersurface singularities I, Invent. Math.88 (1987) 153-165. Zbl0617.14033MR877010
  22. [Li] J. Lipman, Rational singularities with applications to algebraic surfaces and unique factorization, Publ. Math. IHES36 (1969) 195-297. Zbl0181.48903MR276239
  23. [Ma1] H. Matsumura, Commutative Algebra, Benjamin, New York, 1970. Zbl0211.06501MR266911
  24. [Ma2] H. Matsumura, Commutative Ring Theory, Cambridge University Press, Cambridge, 1986. Zbl0603.13001MR879273
  25. [NP] V. Nica and D. Popescu, A structure theorem on formally smooth morphisms in positive characteristic, J. of Algebra100 (1986) 436-455. Zbl0604.13003MR840587
  26. [Po1] D. Popescu, General Néron desingularization and approximation, Nagoya Math. J.104 (1986) 85-119. Zbl0592.14014MR868439
  27. [Po2] D. Popescu, Indecomposable Cohen Macaulay modules and their multiplicities, to appear in Trans. AMS. Zbl0725.13009MR979959
  28. [Re] I. Reiten, Finite dimensional algebras and singularities, in Proceedings, Lambrecht 1985, Springer Lecture Notes in Mathematics, 1273 (1987) 35-57. Zbl0639.16017MR915168
  29. [Sc] F.-O. Schreyer, Finite and countable CM-representation type, in Proceedings, Lambrecht 1985, Springer Lecture Notes in Mathematics, 1273 (1987) 9-34. Zbl0719.14024MR915167
  30. [Yo] Y. Yoshino, Brauer-Thrall type theorem for maximal Cohen-Macaulay modules, J. Math. Soc. Japan39 (1987) 719-739. Zbl0615.13008MR905636

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.