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A few theorems on completion of excellent rings(1)

Published online by Cambridge University Press:  22 January 2016

Paolo Valabrega
Paolo Valabrega*
Affiliation:
Istituto Matematico, Politecnico di Torino
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In [2], chap. IV, 2me partie, (7.4.8), Grothendieck considered the following problem: is any m-adic completion of an excellent ring A also excellent?

In [8] I proved that, if A is an algebra of finite type over an arbitrary field k, the answer is positive.

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 61 , July 1976 , pp. 127 - 133
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1976

Footnotes

(1)

The present paper was written while the author was supported by the CNR (section GNSAGA).

References

[1] Greco, S. Two theorems on excellent rings, Nagoya J. vol. 60, (1976).Google Scholar
[2] Grothendieck, A. E.G.A. Publ. I.H.E.S., Paris, 1960.Google Scholar
[3] Matsumura, H. Commutative Algebra, Benjamin, New York, 1970.Google Scholar
[4] Matsumura, H. Formal power series rings over polynomial rings, Number Theory Algebraic Geometry and Commutative Algebra in honour of Y. Akizuki, Tokyo, 1973.Google Scholar
[5] Nomura, M. Formal power series rings over polynomial rings. II, Number Theory Algebraic Geometry and Commutative Algebra in honour of Y. Akizuki, Tokyo, 1973.Google Scholar
[6] Marot, J. Sur les anneaux universellement japonais, C.R. Acad. Sc. Paris, 1973.Google Scholar
[7] Nagata, M. Local Rings, Interscience, New York, 1962.Google Scholar
[8] Valabrega, P. On the excellent property for power series rings over polynomial rings, J. Math, of Kyoto Univ., vol. 15, No. 2, (1975).Google Scholar
[9] Zariski, and Samuel, Commutative Algebra, Van Nostrand, New York, 1960.CrossRefGoogle Scholar