Résultats récents sur l'approximation des morphismes en algèbre commutative

Bernard Teissier

Séminaire Bourbaki (1993-1994)

  • Volume: 36, page 259-282
  • ISSN: 0303-1179

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Teissier, Bernard. "Résultats récents sur l'approximation des morphismes en algèbre commutative." Séminaire Bourbaki 36 (1993-1994): 259-282. <http://eudml.org/doc/110187>.

@article{Teissier1993-1994,
author = {Teissier, Bernard},
journal = {Séminaire Bourbaki},
keywords = {approximation property; Henselian couple; Bass-Quillen conjecture; projective modules},
language = {fre},
pages = {259-282},
publisher = {Société Mathématique de France},
title = {Résultats récents sur l'approximation des morphismes en algèbre commutative},
url = {http://eudml.org/doc/110187},
volume = {36},
year = {1993-1994},
}

TY - JOUR
AU - Teissier, Bernard
TI - Résultats récents sur l'approximation des morphismes en algèbre commutative
JO - Séminaire Bourbaki
PY - 1993-1994
PB - Société Mathématique de France
VL - 36
SP - 259
EP - 282
LA - fre
KW - approximation property; Henselian couple; Bass-Quillen conjecture; projective modules
UR - http://eudml.org/doc/110187
ER -

References

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  1. [1] S. Abhyankar - Two notes on formal power series, Proc. A.M.S.7 (1956), 903-905. Zbl0073.02601MR80647
  2. [2] S. Abhyankar, M. van der Put - Homomorphisms of analytic local rings. J. Reine u. Ang. Math., 242, (1970), 26-60. Zbl0193.00501MR260729
  3. [3] M. André - Artin's Theorem on the solutions of analytic equations in positive characteristic, Manus. Math.15, (1975), 341-347. Zbl0314.13010MR379493
  4. [4] M. André - Homologie des algèbres commutativesSpringer Verlag, BerlinHeidelbergNew York, 1974. Zbl0284.18009MR352220
  5. [5] M. André - Cinq exposés sur la désingularisation, Manuscrit, École Polytechnique Fédérale de Lausanne, Décembre 1991. 
  6. [6] M. Artin - On the solutions of analytic equations, Inventiones Math. (1968), 277-291. Zbl0172.05301MR232018
  7. [7] M. Artin, Algebraic approximation of structures over local rings, Publ. Math. IHES, 36 (1969), 23-58. Zbl0181.48802MR268188
  8. [8] M. Artin - Algebraic structure of power series rings, Contemp. Math.13 (1982), 223-227. Zbl0528.13021MR685955
  9. [9] M. Artin and J. Denef - Smoothing of a ring homomorphism along a section, Arithmetic and Geometry, Vol. II,(in honor of Shafarevitch), Birkhaüser1983, 5-32. Zbl0555.14002MR717604
  10. [10] J. Becker, Exposé on a conjecture of Tougeron, Ann. Inst. Fourier, Grenoble, 27, 4 (1977), 9-27. Zbl0337.14002MR491700
  11. [11] J. Becker - On the composition of power series, Commutative algebra, Fairfax1979, Lect. Notes in Pure and applied Math., No. 68, 159-172, Dekker, 1982. Zbl0514.13015MR655803
  12. [12] J. Becker - J. Denef, L. Lipshitz, and L. van den Dries, Ultraproducts and Approximation in local rings I, Invent. Math.51, (1979), 189-203. Zbl0416.13004MR528023
  13. [13] N. Bourbaki - Algèbre commutative, Chap. 3 , Masson, 1985. 
  14. [14] D. Cerveau - Résultats de type Artin pour les systèmes d'équations holomorphes, Gazette des mathématiciens, 48, 77-95, S.M.F.1991. Zbl0732.34005MR1116891
  15. [15] M. Coste, J. Ruiz, M. Shiota, Approximation in compact Nash manifolds, Prépublication IRMAR, Rennes 1994. MR1342835
  16. [16] J. Denef, D. Harbater - Global approximation in dimension two, Journal of Algebra, Vol. 129, No.1, 1990. Zbl0707.13003MR1037399
  17. [17] R. Elkik - Solutions d'équations à coefficients dans un anneau hensélien, Ann. Sci. ENS, 6 (1973), 553-604. Zbl0327.14001MR345966
  18. [18] J. Frisch, Points de platitude d'un morphisme d'espaces analytiques complexes, Invent. math., 4, (1967), 118-138. Zbl0167.06803MR222336
  19. [19] H. Hironaka - formal line bundle along exceptionnal loci, Algebraic geometry, Bombay, 1968, Oxford U.P. Zbl0205.24802MR262249
  20. [20] A.M. Gabrielov - Formal relations between analytic functions, Funk. Analiz Appl.5 (1971), 64-65. Zbl0254.32009MR302930
  21. [21] M.J. Greenberg - Rational points in henselian discrete valuation rings, Publ. Math. IHES31, (1966). Zbl0146.42201MR191897
  22. [22] A. Grothendieck, J. Dieudonné - EGA IV, seconde partie, § 7. Publ. Math. IHES24 (1965). MR199181
  23. [23] A. Grothendieck, J. Dieudonné - EGA IV, quatrième partie, § 18. Publ. Math. IHES32 (1965). MR199181
  24. [24] M. Hickel - Sur la fonction d'Artin d'un germe analytique, in Complex analysis, Wuppertal1991. K. Diederich ed., Aspects of Math. E 17, F. Vieweg andSohn1991. MR1122174
  25. [25] H. Kurke, T. Mostowski, G. Pfister, D. Popescu and M. Roczen - Die Approximationeigenschaft lokaler Ringe, Springer LNM634, 1978. Zbl0401.13013MR485851
  26. [26] L. Illusie - Complexe cotangent, I. Springer LMN239. 
  27. [27] S. Lang - Some applications of the local uniformization theorem, Amer. J. Math.76, (1954), 362-374. Zbl0058.27201MR62722
  28. [28] H. Lindel - On a question of Bass-Suslin concerning projective modules over polynomial rings, Invent. Math.65 (1981), 319-323. Zbl0477.13006MR641133
  29. [29] T. Mostowski - Topological equivalence between analytic and algebraic sets, Bull. Acad. Pol. Sci. (1984), 393-400. Zbl0579.32007MR782754
  30. [30] A. Néron - Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. IHES. 21 (1964). Zbl0132.41403MR179172
  31. [31] V. Nica et D. Popescu - A structure theorem on formally smooth morphisms in positive characteristic, J. of Algebra100 (1986), 436-455. Zbl0604.13003MR840587
  32. [32] T. Ogoma - General Néron desingularization based on the idea of Popescu, Preprint. Zbl0821.13003MR1282816
  33. [33] A. Ploski - Note on a theorem of M. Artin, Bull. Acad. Polonaise Sci., Ser. Math.22 (1974), 1107-1109. Zbl0302.32002MR367257
  34. [34] D. Popescu - Global form of Néron's p-desingularization, in Week of algebraic Geometry, Bucharest, June 30-July 6, 1980. Teubner Texte, Band 40, Leipzig, 1981. Zbl0481.13002MR712522
  35. [35] D. Popescu - General Neron desingularisation, Nagoya Math. J.100 (1985), 97-126. Zbl0561.14008MR818160
  36. [36] D. Popescu - General Neron desingularisation and approximation, Nagoya Math. J.104 (1986), 85-115. Zbl0592.14014MR868439
  37. [37] D. Popescu - Letter to the Editor, General Neron desingularisation and approximation, Nagoya Math. J.118 (1990), 45-53. Zbl0685.14009MR1060701
  38. [38] D. Quillen - Projective modules over polynomial rings, Invent. Math.36 (1976), 167-171. Zbl0337.13011MR427303
  39. [39] C. Rotthaus - On the approximation property for excellent rings, Inv. Math.88 (1987), 39-63. Zbl0614.13014MR877005
  40. [40] N. Schappacher - Some remarks on a theorem of M.J. Greenberg, in Proc. 1979 Kingston number theory Conf. Queen's Math. Papers (1980), 100-114. Zbl0468.12016MR634684
  41. [41] N. Schappacher - L'inégalité de Lojasiewicz ultramétrique, CRASParis296 (1983), 439-442. Zbl0532.46049MR703916
  42. [42] M. Spivakovsky - Smoothing of ring homomorphisms, approximation theorems, and the Bass-Quillen conjecture. Prépublication, Toronto1993 (version corrigée de Janvier 1994). 
  43. [43] M. Spivakovsky, - Non-existence of the Artin function for henselian pairs, Prépublication. Zbl0803.13005
  44. [44] J-C. Tougeron, Courbes analytiques sur un germe d'espace analytique et applications, Ann. Inst. Fourier, Grenoble, 26, 2 (1976), 117-131. Zbl0318.32005MR414919
  45. [45] J-C. Tougeron, Solutions d'un système d'équations analytiques réelles et applications, Ann. Inst. Fourier, Grenoble, 26, 3 (1976), 109-135. Zbl0338.13025MR432909
  46. [46] O. Zariski, Local uniformization of algebraic varieties, Annals of maths. 41, No. 4, 1940. Zbl0025.21601MR2864

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