Explicit methods for algebraic automorphic forms

代数自守形式的显式方法

• 批准号: EP/J002658/1
• 负责人: Lassina Dembele
• 金额: $ 75.1万
• 依托单位: University of Warwick
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2011
• 资助国家: 英国
• 起止时间: 2011 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ002658%2F1
• 关键词: Explicit; methods; algebraic; automorphic; forms

The Langlands Programme is one of the most ambitious research programmes in modern mathematics. The programme is a vast web of conjectures which connect analysis, algebraic geometry, representation theory and number theory. At the heart of this programme are automorphic forms (analytic objects) and Galois representations (geometric objects). The two sets are related by a series of conjectures whose level of precision varies according to our understanding. The programme warrant our attention as it has far reaching consequences. This project will develop explicit methods for algebraic automorphic forms. By providing concrete examples of automorphic to work with, it will help improve our understanding of many of conjectures in this field. The PI is particularly interested in the mod p Langlands, as he has had some success in this case with the group GL(2).

朗兰兹计划是现代数学中最雄心勃勃的研究计划之一。该计划是一个庞大的网络的acetutures连接分析，代数几何，表示论和数论。这个程序的核心是自守形式（解析对象）和伽罗瓦表示（几何对象）。这两个集合由一系列的结构联系起来，其精确程度根据我们的理解而变化。该方案值得我们注意，因为它具有深远的影响。本计画将发展代数自守形式的显式方法。通过提供自守的具体例子，它将有助于提高我们对该领域许多知识的理解。PI对mod p Langlands特别感兴趣，因为他在GL（2）群的情况下取得了一些成功。

项目成果

Non-paritious Hilbert modular forms

非奇偶希尔伯特模形式

• DOI: 10.48550/arxiv.1612.06625
• 发表时间: 2016
• 作者: Dembele L

On the existence of abelian surfaces with everywhere good reduction

论处处良好还原的阿贝尔曲面的存在性

• DOI: 10.1090/mcom/3692
• 发表时间: 2021
• 期刊: Mathematics of Computation
• 影响因子: 2
• 作者: Dembélé L

Some extensions of the modular method and Fermat equations of signature $(13,13,n)$

模法和签名 $(13,13,n)$ 的费马方程的一些扩展

• DOI: 10.48550/arxiv.1802.04330
• 发表时间: 2018
• 期刊: arXiv e-prints
• 作者: Billerey Nicolas

Theta lifts of Bianchi modular forms and applications to paramodularity

Theta 将 Bianchi 模块化形式和应用提升为准模块化

• DOI: 10.1112/jlms/jdv023
• 发表时间: 2015
• 期刊: Journal of the London Mathematical Society
• 作者: Berger T

Arithmetic Geometry, Number Theory, and Computation

算术几何、数论和计算

• DOI: 10.1007/978-3-030-80914-0_11
• 发表时间: 2021
• 作者: Cremona J