منابع مشابه
Artin Approximation
In 1968, M. Artin proved that any formal power series solution of a system of analytic equations may be approximated by convergent power series solutions. Motivated by this result and a similar result of Płoski, he conjectured that this remains true when we replace the ring of convergent power series by a more general ring. This paper presents the state of the art on this problem, aimed at non-...
متن کاملThe Classical Artin Approximation Theorems
The various Artin approximation theorems assert the existence of power series solutions of a certain quality Q : formal, analytic, algebraic, of systems of equations of the same quality Q, assuming the existence of power series solutions of a weaker quality Q’ < Q : approximated, formal. The results are frequently used in commutative algebra and algebraic geometry. We present a systematic argum...
متن کاملCorrigendum to “the Classical Artin Approximation Theorems”
The purpose of this note is to clarify and complement various places in the article The classical Artin approximation theorems, published in Bull. Amer. Math. Soc. 54 (2017), no. 4, 595–633. A few reasonings in the article may have been difficult to follow or were even problematic. The author is indebted to F. Castro-Jiménez, C. Chiu, R. Ephraim, B. Lamel, S. Perlega, G. Pfister, G. Rond, M. Si...
متن کاملArtin Approximation and Proper Base Change
and an abelian sheaf F of torsion abelian groups on X, the natural base change map gRf∗F ∼ −→ Rf ′ ∗(g F) is an isomorphism. By limit arguments and considerations with geometric stalks as discussed last time, we can arrange that F is a Z/nZ-sheaf for some n > 0 and it suffices to treat the case where S = Spec (A) for a strictly henselian local ring and S′ = Spec (k′) for a separably closed fiel...
متن کاملArtin Approximation via the Model Theory of Cohen-macaulay Rings
We show the existence of a first order theory Cmd,e whose Noetherian models are precisely the local Cohen-Macaulay rings of dimension d and multiplicity e. The completion of a model of Cmd,e is again a model and is moreover Noetherian. If R is an equicharacteristic local Gorenstein ring of dimension d and multiplicity e with algebraically closed residue field and if the Artin Approximation Prop...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Singularities
سال: 2018
ISSN: 1949-2006
DOI: 10.5427/jsing.2018.17g