中国科学院数学与系统科学研究院
数学研究所
学术报告
代数几何研讨班
Speaker: 扶先辉 教授 (东北师范大学)
Title: Ghosts, phantoms and Cartan-Eilenberg homological algebra for a DG-ring
Time&Venue: 2024年11月29日9：00-10：00 & 思源楼 S817
Abstract: We firstly investigate the ghost ideal and the phantom ideal in the (derived) category of DG-modules of a DG-ring. This allows us to introduce and investigate the notions of a Cartan-Eilenberg projective module, a Cartan-Eilenberg injective module, and a Cartan-Eilenberg flat module for a DG-ring. An immediate application is that we can give an affirmative answer to a conjecture of Minamoto. Also we may investigate Notherian DG-ring from our approach, and parallel to classical theory of rings and modules, introduce and investigate the notions of a coherent DG-ring, and a perfect DG-ring. We also investigate the global dimension and weakly global dimension of a DG-ring in the sense of Hovey and Lockridge. This talk is based on an ongoing project with Wei Hu amd Xiaoyan Yang.
Speaker: 张磊 副教授 (中山大学珠海分校)
Title: The Pro-étale Fundamental Group
Time&Venue: 2024年11月29日10：10-11：10
Venue: 思源楼 S817
Abstract: B. Bhatt and P. Scholze introduced the notion of the pro-étale fundamental group for a topologically Noetherian scheme X in their celebrated work "The pro-étale cohomology for schemes". This is a topological group that classifies the geometric covers of X. Under the Yoneda embedding, the geometric covers are identified with sheaves of sets which are locally constant sheaves for the pro-étale topology. In particular, the finite étale covers are geometric. Therefore, the pro-étale fundamental group refines Grothendieck's étale fundamental group which classifies only finite étale covers. In this talk, we will introduce some comparison theorems about the pro-étale fundamental group in the complex analytic and the p-adic settings. The techniques we are using here are h-descent of the étale site and dévisage.
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