Abhyankar places admit local uniformization in any characteristic

Hagen Knaf; Franz-Viktor Kuhlmann

Annales scientifiques de l'École Normale Supérieure (2005)

  • Volume: 38, Issue: 6, page 833-846
  • ISSN: 0012-9593

How to cite


Knaf, Hagen, and Kuhlmann, Franz-Viktor. "Abhyankar places admit local uniformization in any characteristic." Annales scientifiques de l'École Normale Supérieure 38.6 (2005): 833-846. <http://eudml.org/doc/82676>.

author = {Knaf, Hagen, Kuhlmann, Franz-Viktor},
journal = {Annales scientifiques de l'École Normale Supérieure},
language = {eng},
number = {6},
pages = {833-846},
publisher = {Elsevier},
title = {Abhyankar places admit local uniformization in any characteristic},
url = {http://eudml.org/doc/82676},
volume = {38},
year = {2005},

AU - Knaf, Hagen
AU - Kuhlmann, Franz-Viktor
TI - Abhyankar places admit local uniformization in any characteristic
JO - Annales scientifiques de l'École Normale Supérieure
PY - 2005
PB - Elsevier
VL - 38
IS - 6
SP - 833
EP - 846
LA - eng
UR - http://eudml.org/doc/82676
ER -


  1. [1] Abhyankar S., Uniformization in p-cyclic extensions of a two-dimensional regular local domain of residue field characteristic p, in: Festschrift zur Gedächtnisfeier für Karl Weierstraß 1815–1965, Wissenschaftliche Abhandlungen des Landes Nordrhein-Westfalen, vol. 33, Westdeutscher, Köln und Opladen, 1966, pp. 243-317. Zbl0144.03104MR200273
  2. [2] Abhyankar S., An algorithm on polynomials in one indeterminate with coefficients in a two dimensional regular local domain, Ann. Mat. Pura Appl. (4)71 (1966) 25-59. Zbl0158.04201MR207699
  3. [3] Abhyankar S., Resolution of Singularities of Embedded Algebraic Surfaces, Academic Press, New York, 1966, Springer, New York, 1998. Zbl0147.20504MR1617523
  4. [4] Abhyankar S., Local uniformization on algebraic surfaces over ground fields of characteristic p 0 , Ann. of Math.63 (1956) 491-526. Zbl0108.16803MR78017
  5. [5] Abhyankar S., Resolution of Singularities of Arithmetical Surfaces, Arithmetical Algebraic Geometry, Harper and Row, New York, 1965. Zbl0147.20503MR200272
  6. [6] Abhyankar S., Uniformization of Jungian local domains, Math. Ann.159 (1965) 1-43. Zbl0127.01702MR177989
  7. [7] Bourbaki N., Commutative Algebra, Hermann, Paris, 1972. MR360549
  8. [8] de Jong A.J., Smoothness, semi-stability and alterations, Publ. Math. IHÉS83 (1996) 51-93. Zbl0916.14005MR1423020
  9. [9] Elliott G.A., On totally ordered groups, and K 0 , in: Handelman D., Lawrence J. (Eds.), Ring Theory, Waterloo, 1978, Lecture Notes Math., vol. 734, Springer, Berlin, 1979, pp. 1-49. Zbl0418.06010MR548122
  10. [10] Endler O., Valuation Theory, Springer, Berlin, 1972. Zbl0257.12111MR357379
  11. [11] Fu D., Local weak simultaneous resolution for high rational ranks, J. Algebra194 (1996) 614-630. Zbl0931.13001MR1467169
  12. [12] Heinzer W., Rotthaus C., Wiegand S., Approximating discrete valuation rings by regular local rings, Proc. Amer. Math. Soc.129 (1) (2001) 37-43. Zbl0962.13017MR1694346
  13. [13] Knaf, H., Kuhlmann, F.-V., Every place admits local uniformization in a finite extension of the function field, in preparation. Zbl1221.14016
  14. [14] Kuhlmann, F.-V., On local uniformization in arbitrary characteristic, The Fields Institute Preprint Series, Toronto, 1997. 
  15. [15] Kuhlmann F.-V., Valuation theoretic and model theoretic aspects of local uniformization, in: Hauser H., Lipman J., Oort F., Quiros A. (Eds.), Resolution of Singularities—A Research Textbook in Tribute to Oscar Zariski, Progr. Math., vol. 181, Birkhäuser, Basel, 2000, pp. 381-456. Zbl1046.14001
  16. [16] Kuhlmann F.-V., Places of algebraic function fields in arbitrary characteristic, Adv. Math.188 (2004) 399-424. Zbl1134.12304MR2087232
  17. [17] Kuhlmann, F.-V., Elimination of ramification in valued function fields I: The generalized stability theorem, submitted for publication. 
  18. [18] Ribenboim P., Théorie des valuations, Les Presses de l'Université de Montréal, 1964. Zbl0139.26201MR249425
  19. [19] Raynaud M., Anneaux locaux henséliens, Lecture Notes in Math., vol. 169, Springer, Berlin, 1970. Zbl0203.05102MR277519
  20. [20] Zariski O., Local uniformization on algebraic varieties, Ann. of Math.41 (1940) 852-896. Zbl0025.21601MR2864
  21. [21] Zariski O., The reduction of singularities of an algebraic surface, Ann. of Math.40 (1939) 639-689. Zbl0021.25303MR159
  22. [22] Zariski O., A simplified proof for resolution of singularities of an algebraic surface, Ann. of Math.43 (1942) 583-593. Zbl0063.08389MR6851

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