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arxiv: 1804.08160 · v1 · pith:6HIYUXZMnew · submitted 2018-04-22 · 🧮 math.AG

Echelons of power series and Gabrielov's counterexample to nested linear Artin Approximation

classification 🧮 math.AG
keywords approximationartinechelonsgabrielovnestedpowerseriesanalytic
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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 of ideals in power series rings.

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