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Formal moduli spaces of p-divisible groups in residue characteristic 2

留数特征 2 中 p 可整群的形式模空间

基本信息

批准号：
320227379
负责人：
Dr. Daniel Kirch
金额：
--
依托单位：
Institut de Mathématiques de Jussieu-Paris Rive Gauche (UMR 7586)
依托单位国家：
德国
项目类别：
Research Fellowships
财政年份：
2016
资助国家：
德国
起止时间：
2015-12-31 至 2016-12-31
项目状态：
已结题

来源：
https://gepris.dfg.de/gepris/projekt/320227379?language=en
关键词：
Formal moduli spaces divisible groups

项目摘要

My project is part of the field of arithmetic algebraic geometry, more precisely it lies in the intersection of algebraic number theory, algebraic geometry and the theory of Shimura varieties. The objects of study are formal moduli spaces of p-divisible groups. These moduli spaces are defined by Rapoport and Zink. One application of these spaces is the uniformization of Shimura varieties and the study of their reduction, but their cohomology is also interesting in the context of local Langlands correspondences (cp. work of Fargues, Mantovan and Scholze).The definition by Rapoport and Zink includes moduli spaces of type EL (i.e. with extra data in form of endomorphisms and level structures) and of type PEL (like EL, with polarizations in addition) in the case p>2.The exclusion of residue characteristic 2 is a significant gap in this theory. A general definition (independent of the residue characteristic) would not only justify the theory of Rapoport-Zink spaces and their various (conjectural) generalizations (by Rapoport & Viehmann, Kim, Howard & Pappas), it is also essential for the study of special cycles on Shimura varieties in the context of the Kudla program.In my project I want to attempt a construction of such moduli spaces of type PEL in the case of residue characteristic 2. This project builds upon my PhD thesis, where I already defined a moduli spaces for a unitary group in two variables over a ramified quadratic extension. A first milestone would be the generalization of this result to unitary groups in more variables.

我的项目是算术代数几何领域的一部分，更准确地说，它是代数数论、代数几何和下村变元理论的交集。研究对象是p-可分群的形式模空间。这些模空间由Rapoport和Zink定义。这些空间的一个应用是Shimura簇的均匀化和它们的约化的研究，但它们的上同调在局部Langland对应的上下文中也很有趣(cp.Rapoport和Zink的定义包括EL型的模空间(即具有自同态和能级结构形式的额外数据)和PEL型的模空间(如EL，另外还有极化)。一个一般的定义(与剩余特征无关)不仅证明了Rapoport-Zink空间的理论及其各种(猜想)推广(由Rapoport&Viehmann，Kim，Howard&Pappas提出)，而且对于在Kudla程序中研究Shimura簇的特殊循环也是必不可少的。在我的项目中，我想尝试在剩余特征为2的情况下构造这样的PEL型模空间。这个项目建立在我的博士论文的基础上，其中我已经在分支二次扩张上定义了具有两个变量的酉群的模空间。第一个里程碑是将这一结果推广到变量更多的酉群。