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Completions of Quasi-excellent Domains

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arxiv 2310.00479 v1 pith:H7DHX3PO submitted 2023-09-30 math.AC

David Baron , Ammar Eltigani , S. Loepp , AnaMaria Perez , M. Teplitskiy This is my paper · ORCID
classification math.AC
keywords localquasi-excellentdomainscompletionconditionsdomainnecessaryresults
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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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