Article
Linear nested Artin approximation theorem for algebraic power series
Author/s | Castro Jiménez, Francisco Jesús
![]() ![]() ![]() ![]() ![]() ![]() ![]() Popescu, Dorin Rond, Guillaume |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2018 |
Deposit Date | 2018-05-11 |
Published in |
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Abstract | 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 ... 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. |
Project ID. | MTM2013-40455-P
![]() ID-PCE-2011-1023 ![]() ANR-2011 BS01 009 ![]() ANR-12-JS01-0002-01 ![]() |
Citation | Castro Jiménez, F.J., Popescu, D. y Rond, G. (2018). Linear nested Artin approximation theorem for algebraic power series. Manuscripta mathematica, 1-19. |
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