Integral p_adic Hodge-theory and applications to p-adic deformation theory

积分 p_adic Hodge 理论及其在 p-adic 变形理论中的应用

• 批准号: EP/T005351/1
• 负责人: Andreas Langer
• 金额: $ 48.67万
• 依托单位: UNIVERSITY OF EXETER
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FT005351%2F1
• 关键词: Integral; p_adic; Hodge; theory; applications

We associate linear data to geometric objects like curves, surfaces or threefolds defined as zero-sets of algebraic equations over the integers or over a number domain that is annihilated by a power of a prime number. One can ask how much information about the original object can be captured in this way. The linear data are given by various cohomology theories which is a standard technique in many areas in Pure Mathematics including topology, complex and arithmetic geometry. This problem leads to what is called p-adic deformation theory; the project addresses the question in the case of crystalline cohomology or equivalently de Rham-Witt cohomology classes associated to algebraic cycles and how they deform p-adically. A related problem of particular interest is to identify an integral structure defined over the (p-adic) integers inside these linear data which leads to finer invariants of the geometric objects and encode more information. This method is very common in arithmetic geometry.

我们将线性数据与几何对象相关联，如曲线，曲面或三重定义为整数或素数幂零的数域上的代数方程的零集。人们可以问，以这种方式可以捕获多少关于原始对象的信息。线性数据由各种上同调理论给出，这是纯数学中许多领域的标准技术，包括拓扑学，复几何和算术几何。这个问题导致了所谓的p-adic变形理论;该项目解决了结晶上同调或等价地与代数圈相关的de Rham-Witt上同调类以及它们如何变形的问题。特别感兴趣的一个相关问题是识别在这些线性数据内的（p-adic）整数上定义的积分结构，这导致几何对象的更精细的不变量并编码更多的信息。这种方法在算术几何中很常见。

项目成果

Crystals of relative displays and Calabi-Yau threefolds

相关显示和卡拉比-丘三倍的晶体

• DOI: 10.1016/j.jnt.2022.01.001
• 发表时间: 2022
• 期刊: Journal of Number Theory
• 影响因子: 0.7
• 作者: Gregory O

Hodge-Witt decomposition of relative crystalline cohomology

相对晶体上同调的 Hodge-Witt 分解

• DOI: 10.1112/jlms.12679
• 发表时间: 2022
• 期刊: Journal of the London Mathematical Society
• 作者: Gregory O

An approach for comparing agricultural development to societal visions.

将农业发展与社会愿景进行比较的方法。

• DOI: 10.1007/978-3-319-99423-9_5
• 发表时间: 2022
• 期刊: Agronomy for sustainable development
• 影响因子: 7.3
• 作者: Helfenstein J

Overconvergent de Rham-Witt cohomology for semistable varieties

半稳定簇的过收敛 de Rham-Witt 上同调

• 发表时间: 2020
• 期刊: Muenster Journal of Mathematics
• 影响因子: 0.5
• 作者: Gregory, Oliver;Langer, Andreas
• 通讯作者: Langer, Andreas

Motivic cohomology and K-theory of some surfaces over finite fields

有限域上某些曲面的动机上同调和 K 理论

• DOI: 10.1016/j.jpaa.2023.107518
• 发表时间: 2024
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: Gregory O