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Uniformization in a p-cyclic extension of a two dimensional regular local domain of residue field characteristic p

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Karl Weierstraß, the prince of analysis, was an algebraist. His spirit lives in POWER SERIES. We dedicate this paper to Weierstraß on the occasion of his one hundred and fiftieth birthday.

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References

  1. S. Abhyankar, Local uniformization on algebraic surfaces over ground fields of characteristic p ≠ 0. Annals of Mathematics, vol. 63 (1956), pp. 491–526. Corrections. Annals of Mathematics, vol. 78 (1963), pp. 202–203.

    Article  MathSciNet  MATH  Google Scholar 

  2. On the valuations centered in a local domain. American Journal of Mathematics, vol. 78 (1956), pp. 321–348.

    Google Scholar 

  3. On the field of definition of a nonsingular birational transform of an algebraic surface. Annals of Mathematics, vol. 68 (1957), pp. 268–281.

    Google Scholar 

  4. Ramification theoretic methods in algebraic geometry. Princeton University Press, Princeton 1959.

    Google Scholar 

  5. Tame coverings and fundamental groups of algebraic varieties, Part II: Branch curves with higher singularities. American Journal of Mathematics, vol. 82 (1960), pp. 120–178.

    Google Scholar 

  6. Uniformization in p-cyclic extensions of algebraic surfaces over ground fields of characteristic p. Mathematische Annalen, vol. 153 (1964), pp. 81–96.

    Google Scholar 

  7. Reduction to multiplicity less than p is a p-cyclic extension of a two dimensional regular local ring (p = characteristic of the residue field). Mathematische Annalen, vol. 154 (1964), pp. 28–55.

    Google Scholar 

  8. Uniformization of Jungian local domains. Mathematische Annalen, vol. 159 (1965), pp. 1–43.

    Google Scholar 

  9. A. A. Albert, Modern Higher Algebra. Chicago University Press, Chicago 1937.

    Google Scholar 

  10. C. Chevalley, On the theory of local rings. Annals of Mathematics, vol. 44 (1943), pp. 690–708.

    Article  MathSciNet  MATH  Google Scholar 

  11. I. S. Cohen, On the structure and ideal theory of complete local rings. Transactions of the American Mathematical Society, vol. 57 (1946), pp. 54–106.

    Article  Google Scholar 

  12. W. Krull, Die allgemeine Diskriminantensatz. Mathematische Zeitschrift, vol. 45 (1939), pp. 1–19.

    Article  MathSciNet  Google Scholar 

  13. M. Nagata, Local Rings. Interscience Publishers, New York 1962.

    MATH  Google Scholar 

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Heinrich Behnke Klaus Kopfermann

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© 1966 Springer Fachmedien Wiesbaden

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Abhyankar, S.S. (1966). Uniformization in a p-cyclic extension of a two dimensional regular local domain of residue field characteristic p . In: Behnke, H., Kopfermann, K. (eds) Festschrift zur Gedächtnisfeier für Karl Weierstraß 1815–1965. Wissenschaftliche Abhandlungen der Arbeitsgemeinschaft für Forschung des Landes Nordrhein-Westfalen. VS Verlag für Sozialwissenschaften, Wiesbaden. https://doi.org/10.1007/978-3-663-16281-0_12

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  • DOI: https://doi.org/10.1007/978-3-663-16281-0_12

  • Publisher Name: VS Verlag für Sozialwissenschaften, Wiesbaden

  • Print ISBN: 978-3-663-15697-0

  • Online ISBN: 978-3-663-16281-0

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