Related papers: Artin approximation property and the General Neron…
It gives some new forms of General Neron Desingularization and new applications.
An algorithmic proof of General Neron Desingularization is given here for one dimensional local rings and it is implemented in Singular. Also a theorem recalling Greenberg' strong approximation theorem is presented for one dimensional local…
An algorithmic proof of General Neron Desingularization is given here for one dimensional local domains and it is implemented in \textsc{Singular}. Also a theorem recalling Greenberg' strong approximation theorem is presented for one…
In this paper we give an easy proof of the general Neron desingularization in the frame of regular morphism between Artinian local rings and Noetherian local rings of dimension one.
In this form will appear in Communications in Algebra.
An algorithmic proof of the General Neron Desingularization theorem is given for $2$-dimensional local rings and morphisms with small singular locus.
We study the Artin Approximation property with constraints in a different frame. As a consequence we give a nested Artin Strong Approximation property for algebraic power series rings over a field.
A short proof of the linear nested Artin approximation property of the algebraic power series rings is given here.
We give algorithms to construct the N\'eron Desingularization and the easy case from \cite{KK} of the General N\'eron Desingularization.
An algorithmic proof of the General N\'eron Desingularization theorem and its uniform version is given for morphisms with big smooth locus. This generalizes the results for the one-dimensional case.
Over the last decade, implementations of several desingularization algorithms have appeared in various contexts. These differ as widely in their methods and in their practical efficiency as they differ in the situations in which they may be…
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
It is shown that the derived dimension of any representation-finite Artin algebra is at most one.
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…
We generalize Artin's three main algebraicity theorems to the setting of supergeometry: Artin approximation, algebraization of formal moduli, and algebraization of stacks.
We present a survey on the recent progress with desingularization of quasi-excellent schemes of characteristic zero. Due to expository goals of the paper we concentrate on giving examples and outlining main ideas, and we refer to other…
We give a systematic, abstract formulation of the image normalization method as applied to a general group of image transformations, and then illustrate the abstract analysis by applying it to the hierarchy of viewing transformations of a…
There are abundant results on Diophantine approximation over fields of positive characteristic (see the survey papers [13, 25]), but there is very little information about simultaneous approximation. In this paper, we develop a technique of…
Let X be a singular affine normal variety with coordinate ring R and assume that there is an R-order admitting a stability structure such that the scheme of relevant semistable representations is smooth, then we construct a partial…
The extension dimensions of an Artin algebra give a reasonable way of measuring how far an algebra is from being representation-finite. In this paper we mainly study extension dimensions linked by recollements of derived module categories…