Regular rings and perfect(oid) algebras
Regular rings and perfect(oid) algebras
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DOI：
10.1080/00927872.2018.1524009
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发表时间：
2018-03
影响因子：
0.7
通讯作者：
B. Bhatt;S. Iyengar;Linquan Ma
中科院分区：
文献类型：
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作者：
B. Bhatt;S. Iyengar;Linquan Ma
本文证明了Kunz定理的一个p-adic类比：一个p-adic完备的Noether环，当它允许一个忠实平坦映射到一个完美环时，它是正则的。这一结果是从一个更精确的陈述推出的检测有限性的投影维数的诺特环上的生成模通过映射到perfectoid环。我们还建立了一个版本的p-adic昆兹定理的平坦性假设放宽到几乎平坦。
Abstract We prove a p-adic analog of Kunz’s theorem: a p-adically complete noetherian ring is regular exactly when it admits a faithfully flat map to a perfectoid ring. This result is deduced from a more precise statement on detecting finiteness of projective dimension of finitely generated modules over noetherian rings via maps to perfectoid rings. We also establish a version of the p-adic Kunz’s theorem where the flatness hypothesis is relaxed to almost flatness.