Résultats récents sur l'approximation des morphismes en algèbre commutative
Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 784, 24 p.
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Teissier, Bernard. Résultats récents sur l'approximation des morphismes en algèbre commutative, dans Séminaire Bourbaki : volume 1993/94, exposés 775-789, Astérisque, no. 227 (1995), Exposé no. 784, 24 p. http://archive.numdam.org/item/SB_1993-1994__36__259_0/

[1] S. Abhyankar - Two notes on formal power series, Proc. A.M.S. 7 (1956), 903-905. | DOI | MR | Zbl

[2] S. Abhyankar, M. Van Der Put - Homomorphisms of analytic local rings. J. Reine u. Ang. Math., 242, (1970), 26-60. | EuDML | MR | Zbl

[3] M. André - Artin's Theorem on the solutions of analytic equations in positive characteristic, Manus. Math. 15, (1975), 341-347. | DOI | EuDML | MR | Zbl

[4] M. André - Homologie des algèbres commutatives Springer Verlag, Berlin Heidelberg New York, 1974. | MR | Zbl

[5] M. André - Cinq exposés sur la désingularisation, Manuscrit, École Polytechnique Fédérale de Lausanne, Décembre 1991.

[6] M. Artin - On the solutions of analytic equations, Inventiones Math. (1968), 277-291. | DOI | EuDML | MR | Zbl

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

[8] M. Artin - Algebraic structure of power series rings, Contemp. Math.13 (1982), 223-227. | MR | Zbl

[9] M. Artin and J. Denef - Smoothing of a ring homomorphism along a section, Arithmetic and Geometry, Vol. II,(in honor of Shafarevitch), Birkhaüser 1983, 5-32. | MR | Zbl

[10] J. Becker, Exposé on a conjecture of Tougeron, Ann. Inst. Fourier, Grenoble, 27, 4 (1977), 9-27. | Numdam | MR | Zbl

[11] J. Becker - On the composition of power series, Commutative algebra, Fairfax 1979, Lect. Notes in Pure and applied Math., No. 68, 159-172, Dekker, 1982. | MR | Zbl

[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. | MR | Zbl

[13] N. Bourbaki - Algèbre commutative, Chap. 3 , Masson, 1985.

[14] D. Cerveau - Résultats de type Artin pour les systèmes d'équations holomorphes, Gazette des mathématiciens, 48, 77-95, S.M.F. 1991. | MR | Zbl

[15] M. Coste, J. Ruiz, M. Shiota, Approximation in compact Nash manifolds, Prépublication IRMAR, Rennes 1994. | MR

[16] J. Denef, D. Harbater - Global approximation in dimension two, Journal of Algebra, Vol. 129, No.1, 1990. | MR | Zbl

[17] R. Elkik - Solutions d'équations à coefficients dans un anneau hensélien, Ann. Sci. ENS, 6 (1973), 553-604. | Numdam | MR | Zbl

[18] J. Frisch, Points de platitude d'un morphisme d'espaces analytiques complexes, Invent. math., 4, (1967), 118-138. | MR | Zbl

[19] H. Hironaka - formal line bundle along exceptionnal loci, Algebraic geometry, Bombay, 1968, Oxford U.P. | MR | Zbl

[20] A. M. Gabrielov - Formal relations between analytic functions, Funk. Analiz Appl. 5 (1971), 64-65. | MR | Zbl

[21] M. J. Greenberg - Rational points in henselian discrete valuation rings, Publ. Math. IHES 31, (1966). | Numdam | MR | Zbl

[22] A. Grothendieck, J. Dieudonné - EGA IV, seconde partie, § 7. Publ. Math. IHES 24 (1965). | MR

[23] A. Grothendieck, J. Dieudonné - EGA IV, quatrième partie, § 18. Publ. Math. IHES 32 (1965). | MR

[24] M. Hickel - Sur la fonction d'Artin d'un germe analytique, in Complex analysis, Wuppertal 1991. K. Diederich ed., Aspects of Math. E 17, F. Vieweg andSohn 1991. | MR

[25] H. Kurke, T. Mostowski, G. Pfister, D. Popescu and M. Roczen - Die Approximationeigenschaft lokaler Ringe, Springer LNM 634, 1978. | MR | Zbl

[26] L. Illusie - Complexe cotangent, I. Springer LMN 239.

[27] S. Lang - Some applications of the local uniformization theorem, Amer. J. Math. 76, (1954), 362-374. | MR | Zbl

[28] H. Lindel - On a question of Bass-Suslin concerning projective modules over polynomial rings, Invent. Math. 65 (1981), 319-323. | MR | Zbl

[29] T. Mostowski - Topological equivalence between analytic and algebraic sets, Bull. Acad. Pol. Sci. (1984), 393-400. | MR | Zbl

[30] A. Néron - Modèles minimaux des variétés abéliennes sur les corps locaux et globaux, Publ. Math. IHES. 21 (1964). | Numdam | MR | Zbl

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

[32] T. Ogoma - General Néron desingularization based on the idea of Popescu, Preprint. | MR | Zbl

[33] A. Ploski - Note on a theorem of M. Artin, Bull. Acad. Polonaise Sci., Ser. Math. 22 (1974), 1107-1109. | MR | Zbl

[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. | MR | Zbl

[35] D. Popescu - General Neron desingularisation, Nagoya Math. J. 100 (1985), 97-126. | DOI | MR | Zbl

[36] D. Popescu - General Neron desingularisation and approximation, Nagoya Math. J. 104 (1986), 85-115. | DOI | MR | Zbl

[37] D. Popescu - Letter to the Editor, General Neron desingularisation and approximation, Nagoya Math. J. 118 (1990), 45-53. | DOI | MR | Zbl

[38] D. Quillen - Projective modules over polynomial rings, Invent. Math. 36 (1976), 167-171. | DOI | EuDML | MR | Zbl

[39] C. Rotthaus - On the approximation property for excellent rings, Inv. Math. 88 (1987), 39-63. | DOI | EuDML | MR | Zbl

[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. | MR | Zbl

[41] N. Schappacher - L'inégalité de Lojasiewicz ultramétrique, CRAS Paris 296 (1983), 439-442. | MR | Zbl

[42] M. Spivakovsky - Smoothing of ring homomorphisms, approximation theorems, and the Bass-Quillen conjecture. Prépublication, Toronto 1993 (version corrigée de Janvier 1994).

[43] M. Spivakovsky, - Non-existence of the Artin function for henselian pairs, Prépublication. | DOI | Zbl

[44] J-C. Tougeron, Courbes analytiques sur un germe d'espace analytique et applications, Ann. Inst. Fourier, Grenoble, 26, 2 (1976), 117-131. | DOI | EuDML | Numdam | MR | Zbl

[45] J-C. Tougeron, Solutions d'un système d'équations analytiques réelles et applications, Ann. Inst. Fourier, Grenoble, 26, 3 (1976), 109-135. | DOI | EuDML | Numdam | MR | Zbl

[46] O. Zariski, Local uniformization of algebraic varieties, Annals of maths. 41, No. 4, 1940. | DOI | JFM | MR | Zbl