Related papers: Nested Artin Strong Approximation Property

A short proof of the linear nested Artin approximation property of the algebraic power series rings is given here.

We give a new and 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…

This is an exposition on the General Neron Desingularization and its applications. We end with a recent constructive form of this desingularization in dimension one

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 P{\l}oski, he conjectured that this…

In this paper, we introduce a strong property $(A)$ and we study the transfer of property $(A)$ and strong property $(A)$ in trivial ring extensions and amalgamated duplication of a ring along an ideal. We also exhibit a class of rings…

We extend some parts of the representation theory for integral quadratic forms over the ring of integers of a number field to the case over the coordinate ring $k[C]$ of an affine curve $C$ over a general base field $k$. By using the genus…

In this note we give a simple proof of the fact that local rings of dimension one have the strong uniform Artin-Rees property. Moreover, we give two examples of rings of dimension two where the property fails.

Gabrielov's famous example for the failure of analytic Artin approximation in the presence of nested subring conditions is shown to be due to a growth phenomenon in standard basis computations for echelons, a generalization of the concept…

We deal with the existing problem of filtered multiplicative bases of finite-dimensional associative algebras. For an associative algebra A over a field, we investigate when the property of having a filtered multiplicative basis is…

We construct an algebraic homology functor for Artin stacks of finite type over a field, and we develop intersection-theoretic properties.

We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we give a bound on the dimension of the set of algebraic power…

In this paper, we consider the problem of how to establish algebraic structures on nearness approximation spaces. Essentially, our approach is to define the nearness ring, nearness ideal and nearness ring of all weak cosets by considering…

We give here a result of diophantine approximation between $\O_N$, the ring of power series in several variables, and the completion of the valuation ring that dominates $\O_N$ for the $\m$-adic topology. We deduce from this that the Artin…

We study the notion of strongly badly approximable matrices in the field of power series over a field $K$. We prove a transference principle in this setting, and show that such matrices exist when $K$ is infinite.

We generalize Artin's three main algebraicity theorems to the setting of supergeometry: Artin approximation, algebraization of formal moduli, and algebraization of stacks.

We investigate the padded version of reduction, an extension of multifraction reduction as defined in arXiv:1606.08991, and connect it both with ordinary reduction and with the so-called Property $\mathrm{H}$. As an application, we show…

Matrices are typically considered over fields or rings. Motivated by applications in parametric differential equations and data-driven modeling, we suggest to study matrices with entries from a Hilbert space and present an elementary theory…

This article introduces and studies the tight approximation property, a property of algebraic varieties defined over the function field of a complex or real curve that refines the weak approximation property (and the known cohomological…

In this paper, we study the property of weak approximation with Brauer-Manin obstruction for surfaces with respect to field extensions of number fields. For any nontrivial extension of number fields L/K, assuming a conjecture of M. Stoll,…

We describe the immediate extensions of a one dimensional valuation ring $V$ which could be embedded in some separation of a ultrapower of $V$ with respect to a certain ultrafilter. For such extensions holds a kind of Artin's approximation.