Remarks on Artin approximation with constraints

zbMath1431.13012arXiv1707.08346MaRDI QIDQ2272794

Guillaume Rond, Dorin Popescu

Publication date: 20 September 2019

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1707.08346

zbMATH Keywords

$\aleph_0$-complete fieldapproximations of solutions of polynomial equationsArtin approximations

Mathematics Subject Classification ID

Ultraproducts and related constructions (03C20) Étale and flat extensions; Henselization; Artin approximation (13B40) Power series rings (13J05) Local deformation theory, Artin approximation, etc. (14B12) Ultraproducts and field theory (12L10)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Ultraproducts and approximation in local rings. I
• Power series solutions of algebraic differential equations
• Approximation properties and existential completeness for ring morphisms
• A counterexample to Artin approximation with respect to subrings
• The rank condition and convergence of formal functions
• Model theory
• Nested Artin strong approximation property
• Linear nested Artin approximation theorem for algebraic power series
• Algebraic approximation of structures over complete local rings
• General Néron desingularization and approximation
• Artin Approximation