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Artin Approximation

Commutative Algebra 2018-05-16 v4 Algebraic Geometry Complex Variables

Abstract

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 remains true when the ring of convergent power series is replaced by a more general kind of ring. This paper presents the state of the art on this problem, aimed at non-experts.

Cite

@article{arxiv.1506.04717,
  title  = {Artin Approximation},
  author = {Guillaume Rond},
  journal= {arXiv preprint arXiv:1506.04717},
  year   = {2018}
}

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Final version

R2 v1 2026-06-22T09:53:59.822Z