no. 6
Abhyankar places admit local uniformization in any characteristic
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 6, pp. 833-846. 
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Knaf, Hagen; Kuhlmann, Franz-Viktor. Abhyankar places admit local uniformization in any characteristic. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 38 (2005) no. 6, pp. 833-846. doi : 10.1016/j.ansens.2005.09.001. http://archive.numdam.org/articles/10.1016/j.ansens.2005.09.001/

[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. | MR | Zbl

[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. | MR | Zbl

[3] Abhyankar S., Resolution of Singularities of Embedded Algebraic Surfaces, Academic Press, New York, 1966, Springer, New York, 1998. | MR | Zbl

[4] Abhyankar S., Local uniformization on algebraic surfaces over ground fields of characteristic p≠0, Ann. of Math. 63 (1956) 491-526. | MR | Zbl

[5] Abhyankar S., Resolution of Singularities of Arithmetical Surfaces, Arithmetical Algebraic Geometry, Harper and Row, New York, 1965. | MR | Zbl

[6] Abhyankar S., Uniformization of Jungian local domains, Math. Ann. 159 (1965) 1-43. | MR | Zbl

[7] Bourbaki N., Commutative Algebra, Hermann, Paris, 1972. | MR

[8] De Jong A.J., Smoothness, semi-stability and alterations, Publ. Math. IHÉS 83 (1996) 51-93. | Numdam | MR | Zbl

[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. | MR | Zbl

[10] Endler O., Valuation Theory, Springer, Berlin, 1972. | MR | Zbl

[11] Fu D., Local weak simultaneous resolution for high rational ranks, J. Algebra 194 (1996) 614-630. | MR | Zbl

[12] Heinzer W., Rotthaus C., Wiegand S., Approximating discrete valuation rings by regular local rings, Proc. Amer. Math. Soc. 129 (1) (2001) 37-43. | MR | Zbl

[13] Knaf, H., Kuhlmann, F.-V., Every place admits local uniformization in a finite extension of the function field, in preparation.

[14] Kuhlmann, F.-V., On local uniformization in arbitrary characteristic, The Fields Institute Preprint Series, Toronto, 1997.

[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. | Zbl

[16] Kuhlmann F.-V., Places of algebraic function fields in arbitrary characteristic, Adv. Math. 188 (2004) 399-424. | MR | Zbl

[17] Kuhlmann, F.-V., Elimination of ramification in valued function fields I: The generalized stability theorem, submitted for publication.

[18] Ribenboim P., Théorie des valuations, Les Presses de l'Université de Montréal, 1964. | MR | Zbl

[19] Raynaud M., Anneaux locaux henséliens, Lecture Notes in Math., vol. 169, Springer, Berlin, 1970. | MR | Zbl

[20] Zariski O., Local uniformization on algebraic varieties, Ann. of Math. 41 (1940) 852-896. | MR | Zbl

[21] Zariski O., The reduction of singularities of an algebraic surface, Ann. of Math. 40 (1939) 639-689. | MR | Zbl

[22] Zariski O., A simplified proof for resolution of singularities of an algebraic surface, Ann. of Math. 43 (1942) 583-593. | MR | Zbl

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