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Finitely presented log-regular rings over rank 1 valuation rings

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

余佳弘

时间

2026年03月23日 10:00 至 11:00

地点

Shuangqing-B654

摘要

The theory of log-regular rings, introduced by Kazuya Kato, has become a cornerstone of logarithmic geometry and $p$-adic Hodge theory. By combing the property of fs-monoids and the commutative algebra of regular local rings, Kato's framework provides a notion of "smoothness" for schemes with singularities, such as semistable reduction models. In this talk, we present an extension of Kato's log-regularity to the setting of finitely presented algebras over a general rank 1 valuation ring $\mathcal{O}$. In addition, we establish the essential properties of this class of rings, specifically proving their normality, Hartogs' lemma, and the rigidity (uniqueness) of the log structure.