Upcoming Talks
| 时间地点 | 报告人 | 题目与摘要 |
|---|---|---|
|
4月10日 (周五) 13:30–14:30 SCMS 102） |
范浩程 (Peking University) |
Title. Coherent cohomological dimension of Siegel modular varieties and the modularity of formal Siegel modular forms Abstract. In this talk, we provide an upper bound of the coherent cohomological dimension of the Siegel modular variety. As a corollary, we show that the boundary of the compactified Siegel modular variety satisfies the Grothendieck-Lefschetz condition. This implies, in particular, that every formal Siegel modular forms of genus 𝑔 ≥ 2 and cogenus 1 is classical. |
|
4月10日 (周五) 14:50–15:50 SCMS 102 |
余佳弘 (Morningside Center for Mathematics) |
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 combining 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. |
|
4月10日 (周五) 16:10–17:10 SCMS 102 |
赵和耳 (哈尔滨工业大学数学研究院) |
Title. Monodromies associated to (log) $p$-divisible groups Abstract. Let $R$ be a Henselian DVR with residue field $k$ of characteristic $p>0$ and fraction field $K$, and let $S$ be the standard log trait associated to $R$. In a joint work with Bertapelle and Wang, we established that log $p$-divisible groups over $S$ correspond to $p$-divisible groups with semi-stable reduction over $K$, and also to semi-stable Galois $\mathbb{Z}_p$-representations with Hodge-Tate weights in $\{0,1\}$ (assuming $k$ is perfect and $K$ is a finite extension of $W(k)[1/p]$). In this talk, we discuss mainly the compatibility of monodromies along the correspondences from the joint work. |