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arXiv · 1311.3525

Uniformisation locale des schémas quasi-excellents de caractéristique nulle

Jean-Christophe San Saturnino
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Abstract

We prove an embedded local uniformization theroem for a valuation centered on a point of a quasi-excellent scheme of characteristic zero. The proof reduces to valuations of rank 1 and consists in desingularizing the ideal formed by the elements of infinite value and monomializing the key polynomials. We then prove a monomialization theorem valid in all characteristic under certain conditions, including that of non-existence of limit key polynomials, a condition that is always satified in characteristic zero.

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Jean-Christophe San Saturnino. 2013-11-14. Uniformisation locale des schémas quasi-excellents de caractéristique nulle. https://arxiv.org/abs/1311.3525

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