Geometric Langlands conjecture in de Rham settings

de Rham 设置中的几何朗兰兹猜想

• 批准号: 1101558
• 负责人: Dmytro Arinkin
• 金额: $ 24万
• 依托单位: University of North Carolina at Chapel Hill
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-06-01 至 2014-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1101558&HistoricalAwards=false
• 关键词: Geometric; Langlands; conjecture; de; Rham

The planned research introduces a new formulation of the categorical Langlands correspondence. It replaces the `naive' version of the Langlands correspondence, which is known to specialists to be inconsistent. The principal investigator proposes to study the new statement and verify that it passes natural consistency checks. He then plans to verify the new formulation, starting with some special cases. The investigator also proposes to study the compactified Jacobians of curves with planar singularities and show that they are self-dual. In his earlier work, the principal investigator established the autoduality in the case of reduced irreducible curves; he plans to extend his results to curves that may be reducible and non-reduced.The Langlands program started as a series of conjectures proposed by Robert Langlands beginning in 1967. From its origins in number theory and representation theory, it developed into a framework connecting and influencing many areas of mathematics. In particular, the geometric Langlands program is formulated in terms of algebraic geometry, but can also be interpreted in physical terms as a duality in quantum field theory. This project introduces new geometric ideas into the Langlands program that should resolve some long-standing issues.

计划中的研究引入了一个新的公式的分类朗兰兹对应。它取代了朗兰兹对应的“天真”版本，专家们知道这种版本是不一致的。首席研究员建议研究新的声明，并验证它通过自然一致性检查。然后，他计划从一些特殊情况开始验证新的提法。研究者还提出研究具有平面奇点的曲线的紧化雅可比行列式，并证明它们是自对偶的。在他早期的工作中，主要研究者建立了约化的不可约曲线的自对偶性;他计划将他的结果扩展到可能是可约的和不可约的曲线。朗兰兹纲领开始于1967年由罗伯特·朗兰兹提出的一系列代数。它起源于数论和表示论，后来发展成为连接和影响许多数学领域的框架。特别地，几何朗兰兹程序是用代数几何来表述的，但也可以用物理术语解释为量子场论中的对偶性。该项目将新的几何思想引入朗兰兹纲领，解决了一些长期存在的问题。

项目成果

Formality of derived intersections and the orbifold HKR isomorphism

派生交集的形式和轨道 HKR 同构

• DOI: 10.1016/j.jalgebra.2019.08.002
• 发表时间: 2019
• 期刊: Journal of Algebra
• 影响因子: 0.9
• 作者: Arinkin, Dima;Căldăraru, Andrei;Hablicsek, Márton
• 通讯作者: Hablicsek, Márton