Local Bézout theorem for Henselian rings
- M. Emilia Alonso García
- Henri Lombardi
ISSN: 0010-0757
Année de publication: 2017
Volumen: 68
Fascículo: 3
Pages: 419-432
Type: Article
D'autres publications dans: Collectanea mathematica
Résumé
In this paper we prove what we call Local Bézout Theorem (Theorem 3.7). It is a formal abstract algebraic version, in the frame of Henselian rings and � -adic topology, of a well known theorem in the analytic complex case. This classical theorem says that, given an isolated point of multiplicity r as a zero of a local complete intersection, after deforming the coefficients of these equations we find in a sufficiently small neighborhood of this point exactly r isolated zeroes counted with multiplicities. Our main tools are, first the border bases [11], which turned out to be an efficient computational tool to deal with deformations of algebras. Second we use an important result of de Smit and Lenstra [7], for which there exists a constructive proof in [13]. Using these tools we find a very simple proof of our theorem, which seems new in the classical literature.
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Spanish GR
- MTM-2011-22435
- MTM-2014-55565
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Spanish GR
- MTM-2014-55565
- MTM-2011-22435