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Linear nested Artin approximation theorem for algebraic power series

Opened Access Linear nested Artin approximation theorem for algebraic power series

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Autor: Castro Jiménez, Francisco Jesús
Popescu, Dorin
Rond, Guillaume
Departamento: Universidad de Sevilla. Departamento de álgebra
Fecha: 2018
Publicado en: Manuscripta mathematica, 1-19.
Tipo de documento: Artículo
Resumen: We give an elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subring of the ring of formal power series, we clarify the relationship between this theorem and the problem of the commutation of two operations for ideals: the operation of replacing an ideal by its completion and the operation of replacing an ideal by one of its elimination ideals. In particular we prove that a Grothendieck conjecture about morphisms of analytic/formal algebras and Artin’s question about linear nested approximation problem are equivalent.
Tamaño: 234.1Kb
Formato: PDF

URI: https://hdl.handle.net/11441/74461

DOI: 10.1007/s00229-018-1025-0

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