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==Statement of the theorem==
Let <math>\mathbf{x} = x_1, \dots, x_n</math> denote a collection of ''n'' [[indeterminate (variable)|indeterminate]]s, <math>k[[\mathbf{x}]]</math> the [[ring (mathematics)|ring]] of formal [[power series]] with indeterminates <math>\mathbf{x}</math> over a field ''k'', and <math>\mathbf{y} = y_1, \dots, y_n</math> a different set of indeterminates. Let
:<math>f(\mathbf{x}, \mathbf{y}) = 0</math>
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==References==
*{{Citation | last1=Artin | first1=Michael | author1-link=Michael Artin | title=Algebraic approximation of structures over complete local rings | url=http://www.numdam.org/item?id=PMIHES_1969__36__23_0 | mr=0268188 | year=1969 | journal=[[Publications Mathématiques de l'IHÉS]] | volume=36 | issue=36 | pages=23–58| doi=10.1007/BF02684596 }}
*{{cite book|last=Artin|first= Michael|title=Algebraic Spaces|publisher= [[Yale University Press]]|series=Yale Mathematical Monographs|volume= 3|___location=New Haven, CT–London|year= 1971|mr=0407012}}
*{{citation|last=Raynaud|first= Michel|author-link=Michel Raynaud|title=Travaux récents de M. Artin| journal=[[Séminaire Nicolas Bourbaki]]|volume= 11 |year=1971|issue=363|pages=
[[Category:Moduli theory]]
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