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arXiv · 1301.1154

Asymptotic behaviour of standard bases

Guillaume Rond
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Abstract

We prove here that the elements of any standard basis of $I^n$, where $I$ is an ideal of a Noetherian local ring and $n$ is a positive integer, have order bounded by a linear function in $n$. We deduce from this that the elements of any standard basis of $I^n$ in the sense of Grauert-Hironaka, where $I$ is an ideal of the ring of power series, have order bounded by a polynomial function in $n$.

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Guillaume Rond. 2013-01-07. Asymptotic behaviour of standard bases. https://arxiv.org/abs/1301.1154

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