This is a preview of subscription content, log in via an institution to check access.
References
This was generalized to perfectk in the subsequent paper “On the field of definition of a nonsingular birational transform of an algebraic surface”, Annals of Math., vol. 65 (1957), pp. 268–281. Erratum: on page 279 line 21 of this paper, replace “any finite algebraic” by “any”.
For corrections to §1 to §6 of U see Annals of Math., vol. 78 (1963) pp. 202–203. Although §§ 7, 8, 9 of U contain many misprints we need not give errata to them.
See Theorem 1 on p. 330 of “On the valuations centered in a local domain”, Am. J. Math., vol. 78 (1956).
For the definition and properties of quadratic transforms see § 2 of the paper cited in Footnote 3.
Also see Theorem 2 of the paper cited in Footnote 3.
See Proposition 1.5 in:C. Chevalley, “Some properties of ideals in rings of power series”, Trans. Am. Math. Soc., vol. 55 (1944), pp. 68–84.
See the proof of Proposition 1 of the paper cited in Footnote 1.
Author information
Authors and Affiliations
Additional information
This work was supported by the National Science Foundation under NSF-G 25 225.
Rights and permissions
About this article
Cite this article
Abhyankar, S. Uniformization inp-cyclic extensions of algebraic surfaces over ground fields of characteristicp . Math. Ann. 153, 81–96 (1964). https://doi.org/10.1007/BF01361177
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01361177