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arXiv · 2310.00479

Completions of Quasi-excellent Domains

David Baron·Ammar Eltigani·S. Loepp·AnaMaria Perez·M. Teplitskiy
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Abstract

Let $T$ be a complete local (Noetherian) ring of characteristic zero. We find necessary and sufficient conditions for $T$ to be the completion of a quasi-excellent local domain. In the case that $T$ contains the rationals, we provide necessary and sufficient conditions for $T$ to be the completion of a countable quasi-excellent local domain. We also prove results regarding the possible lengths of maximal saturated chains of prime ideals of these quasi-excellent local domains, and we show that these results lead to interesting examples of noncatenary quasi-excellent local domains.

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David Baron, Ammar Eltigani, S. Loepp, AnaMaria Perez, M. Teplitskiy. 2023-09-30. Completions of Quasi-excellent Domains. https://arxiv.org/abs/2310.00479

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