Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-24T00:47:51.769Z Has data issue: false hasContentIssue false
  • English
  • Français

Descent of P-property by proper surjective morphisms

Published online by Cambridge University Press:  22 January 2016

Tetsushi Ogoma
Tetsushi Ogoma*
Affiliation:
Kochi University, Department of Mathematics, Faculty of Science, Kochi, 780, Japan
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

It is well known that the quasi-exellent property (i.e. G-ring and J-II) ascends by finite type morphisms. On the other hand Greco showed in [2, Proposition 4.1 and Proposition 2.3] that G-property (i.e. formal fibers are geometrically regular) does not descend by finite type morphisms, although J-II property (i.e. any finite type algebra has regular locus open) does.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 92 , December 1983 , pp. 175 - 177
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1983

References

[1] Bellaccini, B., Proper morphisms and excellent schemes, Nagoya Math. J., 89 (1983), 109–118.CrossRefGoogle Scholar
[2] Greco, S., Two theorems on excellent rings, Nagoya Math. J., 60 (1976), 139–149.Google Scholar
[3] Grothendieck, A. and Dieudonné, J., Éléments de Géométrie Algébrique I, II and IV, Publ. Math. I.H.E.S.Google Scholar
[4] Matsumura, H., Commutative algebra, Benjamin Inc., New York, 1970.Google Scholar
[5] Nagata, M., Local rings, John Wiley, New York, 1962 Reprinted Krieger, , Huntington, N.Y., 1975.Google Scholar
[6] Watanabe, K., Ishikawa, T., Tachibana, S. and Otsuka, K., On tensor products of Gorenstein Rings, J. Math. Kyoto Univ., 9 (1969), 413–423.Google Scholar