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arXiv · 2004.08877

Artin approximation over Banach spaces

Guillaume Rond
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Abstract

We give examples showing that the usual Artin Approximation theorems valid for convergent series over a field are no longer true for convergent series over a commutative Banach algebra. In particular we construct an example of a commutative integral Banach algebra $R$ such that the ring of formal power series over $R$ is not flat over the ring of convergent power series over $R$.

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Guillaume Rond. 2020-04-19. Artin approximation over Banach spaces. https://arxiv.org/abs/2004.08877

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