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A direct proof of the theorem on formal functions
Author(s):
Fernando
Sancho de Salas;
Pedro
Sancho de Salas
Journal:
Proc. Amer. Math. Soc.
137
(2009),
4083-4088.
MSC (2000):
Primary 14A15;
Secondary 14F99
Posted:
July 30, 2009
MathSciNet review:
2538569
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Abstract:
We give a direct and elementary proof of the theorem on formal functions by studying the behaviour of the Godement resolution of a sheaf of modules under completion. This proof also works in some non-noetherian cases.
References:
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- [A]
- Atiyah, M.F. and Macdonald, I.G., Introduction to Commutative Algebra, Addison-Wesley Publishing Company, 1969. MR 0242802 (39:4129)
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- Godement, R., Topologie algébrique et théorie des faisceaux, Troisième édition revue et corrigée. Publications de l'Institut de Mathématique de l'Université de Strasbourg, XIII. Actualités Scientifiques et Industrielles, No. 1252. Hermann, Paris, 1973. MR 0345092 (49:9831)
- [Gro]
- Grothendieck, A. and Dieudonné, J., Éléments de géométrie algébrique III, Publ. Math. IHES, 1961. MR 0217085 (36:177c)
- [H]
- Hartshorne, R., Algebraic Geometry, Grad. Texts Math., 52, Springer-Verlag, 1977. MR 0463157 (57:3116)
- [I]
- Illusie, L., Théorie des Intersections et Théorème de Riemann-Roch, Lecture Notes in Math., 225, Springer-Verlag, New York, 1971. MR 0354655 (50:7133)
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- Kiehl, R., Ein ``Descente''-Lemma und Grothendiecks Projektionsatz für nicht-noetheresche Schemata, Math Annalen 198 (1972), 287-316. MR 0382280 (52:3165)
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Additional Information:
Fernando
Sancho de Salas
Affiliation:
Departamento de Matemáticas, Universidad de Salamanca, Plaza de la Merced 1-4, 37008 Salamanca, Spain
Email:
fsancho@usal.es
Pedro
Sancho de Salas
Affiliation:
Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06071 Badajoz, Spain
Email:
sancho@unex.es
DOI:
10.1090/S0002-9939-09-10015-1
PII:
S 0002-9939(09)10015-1
Keywords:
Formal functions,
completion,
cohomology
Received by editor(s):
July 2, 2008,
Received by editor(s) in revised form:
April 26, 2009
Posted:
July 30, 2009
Additional Notes:
The first author was supported by research projects MTM2006-04779 (MEC) and SA001A07 (JCYL)
Communicated by:
Ted Chinburg
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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