Tohoku Mathematical Journal

An elementary proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case

Kazuhiko Kurano and Kazuma Shimomoto

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The aim of this article is to give a new proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case.

Article information

Tohoku Math. J. (2), Volume 70, Number 3 (2018), 377-389.

First available in Project Euclid: 21 September 2018

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 12F10: Separable extensions, Galois theory
Secondary: 13B40: Étale and flat extensions; Henselization; Artin approximation [See also 13J15, 14B12, 14B25] 13J10: Complete rings, completion [See also 13B35]

coefficient field complete local ring differentials $p$-basis


Kurano, Kazuhiko; Shimomoto, Kazuma. An elementary proof of Cohen-Gabber theorem in the equal characteristic $p>0$ case. Tohoku Math. J. (2) 70 (2018), no. 3, 377--389. doi:10.2748/tmj/1537495352.

Export citation


  • N. Bourbaki, Algèbre commutative, Chap. 1–Chap. 9. Hermann, 1961–83.
  • I. S. Cohen, On the structure and ideal theory of complete local rings, Trans. Amer. Math. Soc. 59 (1946), 54–106.
  • O. Gabber and F. Orgogozo, Sur la p-dimension des corps, Invent. Math. 174 (2008), 47–80.
  • S. M. Gersten, A short proof of the algebraic Weierstrass Preparation Theorem, Proc. Amer. Math. Soc. 88 (1983), 751–752.
  • L. Illusie, Y. Laszlo and F. Orgogozo, Travaux de Gabber sur l'uniformisation locale et la cohomologie étale des schémas quasi-excellents, Astérisque No. 363–364 (2014). Société Mathématique de France, Paris, 2014.
  • H. Matsumura, Commutative ring theory, Cambridge Studies in Advanced Mathematics 8, Cambridge University Press, Cambridge, 1986.
  • T. Ochiai and K. Shimomoto, Specialization method in Krull dimension two and Euler system theory over normal deformation rings, to appear in Annales Mathématiques du Québec.
  • I. Swanson and C. Huneke, Integral closure of ideals rings, and modules, London Math. Soc. Lecture Note Ser. 336, Cambridge University Press, Cambridge, 2006.