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References

  1. M. Artin, On algebraic extensions of local rings,Rend. di Mat., 25 (1966), 33–37.

    MathSciNet  Google Scholar 

  2. ——, Etale coverings of schemes over hensel rings,Amer. J. Math., 88 (1966), 915–934.

    Article  MATH  MathSciNet  Google Scholar 

  3. --, The implicit function theorem in algebraic geometry (to appear).

  4. ——, On the solutions of analytic equations,Inventiones Math., 5 (1968), 277–291.

    Article  MATH  MathSciNet  Google Scholar 

  5. --, Algebraization of formal moduli, I, II (to appear).

  6. --,A. Grothendieck andJ.-L. Verdier, Séminaire de géométrie algébrique 1963–1964, Cohomologie étale des schémas,Inst. Hautes Études Sci. (mimeographed notes).

  7. B. J. Birch andK. McCann, A criterion for thep-adic solubility of diophantine equations,Quarterly J. Math., 18 (1967), 59–63.

    Article  MATH  MathSciNet  Google Scholar 

  8. N. Bourbaki,Éléments de Mathématique, Algèbre commutative, chap. III, Paris, Hermann, 1961.

  9. M. Greenberg, Schemata over local rings,Ann. of Math., 73 (1961), 624–648.

    Article  MathSciNet  Google Scholar 

  10. --, Rational points in henselian discrete valuation rings,Publ. Math. Inst. Hautes Études Sci., no 23, 1964.

  11. N. Greenleaf, Irreducible subvarieties and rational points,Amer. J. Math., 87 (1965), 25–31.

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Grothendieck, Le groupe de Brauer, III,Inst. Hautes Études Sci. (mimeographed notes).

  13. G. Hermann, Die Frage der endlich vielen Schritte in der Theorie der Polynomideale,Math. Annalen, 95 (1926), 736–788.

    Article  MATH  MathSciNet  Google Scholar 

  14. H. Hironaka, On the equivalence of singularities: I,Arithmetical algebraic geometry Proceedings, New York, Harper and Row, 1965.

    Google Scholar 

  15. --, Formal line bundles along exceptional loci (to appear).

  16. M. Nagata,Local rings, New York, Interscience, 1962.

    MATH  Google Scholar 

  17. A. Nerode, A decision method forp-adic integral zeros of diophantine equations,Bull. Amer. Math. Soc., 69 (1963), 513–517.

    Article  MATH  MathSciNet  Google Scholar 

  18. A. Néron, Modèles minimaux des variétés abéliennes sur les corps locaux et globaux,Pub. Math. Inst. Hautes Études Sci., no 21, 1964.

  19. P. Samuel, Algébricité de certains points singuliers algébroïdes,J. Math. Pures Appl., 35 (1956), 1–6.

    MATH  MathSciNet  Google Scholar 

  20. G. Stolzenberg (to appear).

  21. J. C. Tougeron,Idéaux de fonctions différentiables (Thèse), Rennes, 1967.

  22. O. Zariski andP. Samuel,Commutative algebra, vol. II, Princeton, Van Nostrand, 1960.

  23. O. Zariski, Equisingular points on algebraic varieties,Seminari dell’Istituto Nazionale di Alta Matematica 1962–1963, Rome, Ed. Cremonese, 1964. EGA,J. Dieudonné andA. Grothendieck, Éléments de géométrie algébrique,Publ. Math. Inst. Hautes Études Sci., 1960–68. SGA,A. Grothendieck, Séminaire de géométrie algébrique, 1960–1961,Inst. Hautes Études Sci. (mimcographed notes). FGA, --,Fondements de la géométrie algébrique, Extraits du Séminaire Bourbaki, 1957–1962 (mimeographed notes).

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Supported by the Sloan Foundation and by the National Science Foundation.

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Artin, M. Algebraic approximation of structures over complete local rings. Publications Mathématiques de l’Institut des Hautes Scientifiques 36, 23–58 (1969). https://doi.org/10.1007/BF02684596

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