Collaborative Research FRG: Automorphic Forms, Galois Representations, and Special Values of L-Functions
协作研究 FRG:自守形式、伽罗瓦表示和 L 函数的特殊值
基本信息
- 批准号:0456300
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2005
- 资助国家:美国
- 起止时间:2005-07-01 至 2007-11-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Number theory has seen many significant advances in the past few years. Results from arithmetic geometry and the theories of modular forms and Galois representations have yielded a proof Fermat's Last Theorem and fundamental advances towards the $p$-adic Birch-Swinnerton-Dyer Conjecture (BSD), to name two. The research proposed in this project aims to continue this progress. The PI's propose to investigate many aspects of the connections between automorphic forms, Galois representations, and values of their $L$-functions, with the particular aim of making advances towards BSD, Bloch-Kato conjectures, and the Iwasawa Theory of automorphic Galois representations, as well as answering fundamental questions about the Galois representations associated to automorphic forms. Their project focuses on $p$-adic methods in the theory of automorphic forms and Galois representations. By combining their various expertise, they propose to consider a number of specific problems that fall under the following headings: $p$-adic Eisenstein measures and their specializations, Iwasawa's $\mu$-invariants, Non-vanishing modulo $p$ of $L$-values, Eisenstein ideals for unitary groups, Geometric construction of $p$-adic automorphic forms, $p$-adic construction of Euler systems, Endoscopic congruences, Galois representations and Shimura varieties. This project will enhance our knowledge of the deep links between automorphic forms, Galois representations, and their $L$-functions - a central focus of number theory - as well as have significant consequences for our understanding of mathematics in general. Two workshops, a final conference, and graduate and post-doctoral advising will have an important impact on the formation of new researchers in the field and on the promotion of new collaborations.
数论在过去几年中取得了许多重大进展。从算术几何和理论的模形式和伽罗瓦表示的结果已经产生了一个证明费马大定理和基本的进步对$p$-adic伯奇-斯温纳顿-戴尔猜想(BSD),仅举两例。本项目中提出的研究旨在继续这一进展。PI的建议,以调查自守形式,伽罗瓦表示,和他们的$L$-函数的值之间的连接的许多方面,特别是对BSD,布洛赫-加藤结构,和岩泽理论的自守伽罗瓦表示的进步的目的,以及回答有关的伽罗瓦表示与自守形式的基本问题。他们的项目集中在自守形式和伽罗瓦表示理论中的$p$-adic方法。通过结合他们的各种专门知识,他们建议审议下列标题下的一些具体问题:$p$-adic Eisenstein测度及其特殊化,Iwasawa的$\mu$-不变量,L$-值的模$p$非零,酉群的Eisenstein理想,$p $-adic自守形式的几何构造,Euler系统的$p $-adic构造,Endoscopic同余,伽罗瓦表示和志村变种。这个项目将增强我们对自守形式,伽罗瓦表示及其$L$-函数之间的深层联系的认识-数论的中心焦点-并对我们对数学的理解产生重大影响。两个研讨会,最后一次会议,研究生和博士后咨询将对该领域新研究人员的形成和促进新的合作产生重要影响。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
Christopher Skinner其他文献
The mid-IR radio correlation at high angular resolution: NGC253
- DOI:
10.1007/bf00430148 - 发表时间:
1994-01-01 - 期刊:
- 影响因子:2.200
- 作者:
Eric Keto;Roger Ball;Christopher Skinner;John Arens;Garrett Jernigan;Margaret Meixner;James Graham - 通讯作者:
James Graham
Christopher Skinner的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('Christopher Skinner', 18)}}的其他基金
L-Values, Special Cycles, and Euler Systems
L 值、特殊循环和欧拉系统
- 批准号:
1901985 - 财政年份:2019
- 资助金额:
-- - 项目类别:
Continuing Grant
Collaborative Research: P2C2--Elucidating the Drivers and Consequences of Changes in Atmospheric Rivers from the Last Glacial Maximum to the Present Day
合作研究:P2C2——阐明从末次盛冰期至今大气河流变化的驱动因素和后果
- 批准号:
1903600 - 财政年份:2019
- 资助金额:
-- - 项目类别:
Standard Grant
The p-adic geometry of Shimura varieties and applications to the Langlands program
Shimura 簇的 p 进几何及其在朗兰兹纲领中的应用
- 批准号:
1501064 - 财政年份:2015
- 资助金额:
-- - 项目类别:
Standard Grant
L-values, Galois representations, and elliptic curves
L 值、伽罗瓦表示和椭圆曲线
- 批准号:
1301842 - 财政年份:2013
- 资助金额:
-- - 项目类别:
Standard Grant
FRG: Collaborative Research: Automorphic forms, Galois representations, periods and p-adic L-functions
FRG:协作研究:自守形式、伽罗瓦表示、周期和 p 进 L 函数
- 批准号:
0854974 - 财政年份:2009
- 资助金额:
-- - 项目类别:
Standard Grant
L-values, Selmer Groups, and Automorphic Forms
L 值、Selmer 群和自守形式
- 批准号:
0701231 - 财政年份:2007
- 资助金额:
-- - 项目类别:
Continuing Grant
Collaborative Research FRG: Automorphic Forms, Galois Representations, and Special Values of L-Functions
协作研究 FRG:自守形式、伽罗瓦表示和 L 函数的特殊值
- 批准号:
0803223 - 财政年份:2007
- 资助金额:
-- - 项目类别:
Standard Grant
L-values, Galois Representations, and Modular Forms
L 值、伽罗瓦表示和模形式
- 批准号:
0245387 - 财政年份:2003
- 资助金额:
-- - 项目类别:
Continuing Grant
相似国自然基金
Research on Quantum Field Theory without a Lagrangian Description
- 批准号:24ZR1403900
- 批准年份:2024
- 资助金额:0.0 万元
- 项目类别:省市级项目
Cell Research
- 批准号:31224802
- 批准年份:2012
- 资助金额:24.0 万元
- 项目类别:专项基金项目
Cell Research
- 批准号:31024804
- 批准年份:2010
- 资助金额:24.0 万元
- 项目类别:专项基金项目
Cell Research (细胞研究)
- 批准号:30824808
- 批准年份:2008
- 资助金额:24.0 万元
- 项目类别:专项基金项目
Research on the Rapid Growth Mechanism of KDP Crystal
- 批准号:10774081
- 批准年份:2007
- 资助金额:45.0 万元
- 项目类别:面上项目
相似海外基金
FRG: Collaborative Research: New birational invariants
FRG:协作研究:新的双有理不变量
- 批准号:
2244978 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245017 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245111 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245077 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2244879 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Standard Grant
FRG: Collaborative Research: New Birational Invariants
FRG:合作研究:新的双理性不变量
- 批准号:
2245171 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Continuing Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2403764 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Standard Grant
FRG: Collaborative Research: Singularities in Incompressible Flows: Computer Assisted Proofs and Physics-Informed Neural Networks
FRG:协作研究:不可压缩流中的奇异性:计算机辅助证明和物理信息神经网络
- 批准号:
2245021 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Standard Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245097 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Continuing Grant
FRG: Collaborative Research: Variationally Stable Neural Networks for Simulation, Learning, and Experimental Design of Complex Physical Systems
FRG:协作研究:用于复杂物理系统仿真、学习和实验设计的变稳定神经网络
- 批准号:
2245147 - 财政年份:2023
- 资助金额:
-- - 项目类别:
Continuing Grant