短课程名称:Lectures on Kisin modules and its applications
主讲人:高辉 博士(北京国际数学研究中心)
时间: 4月25日(周一)下午 14:00—15:30
4月27日(周三)下午 14:00—15:30
4月29日(周五)下午 14:00—15:30
地点:数学楼401室
摘要:
Lecture 1: Survey on some notions of integral p-adic Hodge theory
We firstly quickly review the notion of crystalline representations and Fontaine modules. We will then survey several ``linear algebra categories in integral p-adic Hodge theory, including Fontaine-Laffaille modules, strongly divisible modules, Kisin modules, and (phi, \hat G)-modules. We will try to give some examples, without any proofs.
Lecture 2: Kisin modules, and some applications
We will try to give a sketch of the proof of existence of Kisin modules. We then present some applications of Kisin modules, in particular, its relation with p-divisible groups. If time permits, we also discuss its relation with Galois deformation rings.
Lecture 3: Kisin modules and local models
We will present the work of Caraiani-Levin, which shows that the moduli of Kisin modules with descent data naturally have the structure of local models. If time permits, we will discuss its application to Serre weight conjectures.