Approximation results of Artin-Tougeron-type for general filtrations and for $C^r$-equations

Abstract

Artin approximation and other related approximation results are used in various areas. The traditional formulation of such results is restricted to filtrations by powers of ideals, $\{I^j\}$, and to Noetherian rings. In this paper we extend several approximation results both to rather general filtrations and to $C^r$-rings, for $2\le r\le \infty$. As an auxiliary step we establish the surjectivity of the completion map for rings of $C^{\infty }$ functions, for a very broad class of filtrations.

arXiv commentFinal version, to appear in JPAA

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Cited by in corpus (1)

• Pairs of Lie-type and large orbits of group actions on filtered modules. (A characteristic-free approach to finite determinacy.)