探花视频

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu, Huajie Li

Speaker：

Jiahong Yu 余佳弘 (MCM)

Time：

Mon., 10:00-11:00 am, Mar. 23, 2026

Venue：

C654, Shuangqing Complex Building A

Title：

Finitely presented log-regular rings over rank 1 valuation rings

Abstract:

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 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.