BIMSA >
BIMSA-YMSC Tsinghua Number Theory Seminar
BIMSA-YMSC Tsinghua Number Theory Seminar
Finitely presented log-regular rings over rank 1 valuation rings
Finitely presented log-regular rings over rank 1 valuation rings
Organizers
Hansheng Diao
, Heng Du
, Yueke Hu
, Bin Xu
, Yihang Zhu
Speaker
Jiahong Yu
Time
Monday, March 23, 2026 10:00 AM - 11:00 AM
Venue
Shuangqing-B654
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 $\mathcal{O}$. 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.