197
Views
3
CrossRef citations to date
0
Altmetric
Original Articles

On the Witt Vectors of Perfect Rings in Positive Characteristic

Pages 5328-5342 | Received 17 Jul 2014, Published online: 24 Aug 2015

REFERENCES

  • Artin , M. ( 1971 ). On the joins of Hensel rings . Advances in Math. 7 : 282 – 296 .
  • Asgharzadeh , M. ( 2010 ). Homological properties of the perfect and absolute integral closures of Noetherian domains . Math. Annalen 348 : 237 – 263 .
  • Bourbaki , N. ( 1998 ). Commutative Algebra. Chapter 1–7. Springer .
  • Bruns , W. , Herzog , J. ( 1998 ). Cohen-Macaulay Rings. Vol. 39. Cambridge University Press .
  • Davis , C. , Kedlaya , K. S. ( 2014 ). On the Witt vector Frobenius . Proceedings of the American Mathematical Society 142 : 2211 – 2226 .
  • Dietz , G. D. ( 2007 ). Big Cohen-Macaulay algebras and seeds . Trans. Amer. Math. Soc. 359 : 5959 – 5989 .
  • Glaz , S. ( 1989 ). Commutative Coherent Rings. LNM, Vol. 1371. Springer-Verlag .
  • Heinzer , W. ( 1969 ). Some remarks on complete integral closure . J. Austral. Math. Soc. 9 : 310 – 314 .
  • Hochster , M. ( 2002 ). Big Cohen-Macaulay algebras in dimension three via Heitmann's theorem . J. Algebra 254 : 395 – 408 .
  • Hochster , M. , Huneke , C. ( 1992 ). Infinite integral extensions and big Cohen-Macaulay algebras . Ann. of Math. 135 : 53 – 89 .
  • J\ootndrup, S., Small , L. W. ( 1974 ). Power series over coherent rings . Math. Scand. 35 : 21 – 24 .
  • Kedlaya , K. S. , Liu , R. Relative p-adic Hodge theory. To appear in Astérisque.
  • Kunz , E. ( 1969 ). Characterizations of regular local rings for characteristic p. Amer. J. Math. 91:772–784 .
  • Matsumura , H. ( 1986 ). Commutative Ring Theory. Vol. 8. Cambridge University Press .
  • Rabinoff , J. The theory of Witt vectors, Available at http://www.math.harvard. edu/ᵲabinoff/misc/witt.pdf.
  • Raynaud , M. ( 1970 ). Anneaux Locaux Henséliens. LNM, Vol. 169. Springer-Verlag .
  • Scholze , P. ( 2012 ). Perfectoid spaces . Publ. Math. de l'IHÉS 116 : 245 – 313 .
  • Serre , J.-P. ( 1973 ). Local Fields . Graduate Texts in Mathematics , Vol. 67. New York : Springer-Verlag .
  • Shimomoto , K. ( 2011 ). F-coherent rings with applications to tight closure theory . J. Algebra 338 : 24 – 34 .
  • Shimomoto , K. ( 2011 ). Almost Cohen-Macaulay algebras in mixed characteristic via Fontaine rings . Illinois J. Math. 55 : 107 – 125 .
  • Shimomoto , K. An application of the almost purity theorem to the homological conjectures. Submitted.
  • Strooker , J. R. Homological Questions in Local Algebra. London Math. Society Lecture Note Series, Vol. 145.
  • Swanson , I. , Huneke , C. Integral Closure of Ideals Rings, and Modules. London Math. Society Lecture Note Series, Vol. 336.
  • Yekutieli , A. ( 2011 ). On flatness and completion for infinitely generated modules over Noetherian rings . Comm. Algebra 39 : 4221 – 4245 .
  • Communicated by G. Leuschke.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.