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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A direct proof of the theorem on formal functions


Authors: Fernando Sancho de Salas and Pedro Sancho de Salas
Journal: Proc. Amer. Math. Soc. 137 (2009), 4083-4088
MSC (2000): Primary 14A15; Secondary 14F99
Published electronically: 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.


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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: http://dx.doi.org/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
Published electronically: July 30, 2009
Additional Notes: The first author was supported by research projects MTM2006-04779 (MEC) and SA001A07 (JCYL)
Communicated by: Ted Chinburg
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.