Shimura varieties, Galois representations and Riemann-Roch theorems
Shimura 簇、Galois 表示和 Riemann-Roch 定理
基本信息
- 批准号:0802686
- 负责人:
- 金额:$ 15万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2008
- 资助国家:美国
- 起止时间:2008-06-01 至 2012-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
The principal investigator is working on the following three problems:(A) He is attempting to describe integral models for Shimura varieties at primes of non-smooth reduction. In particular, he studies ``local models" for Shimura varieties and their relation with affine flag varieties for infinite dimensional groups and with deformation spaces of Galois representations. The motivation is to obtain information that can be used in the calculation of the Hasse-Weil zeta function of these varieties and in other number theoretic applications.(B) He is developing refined and functorial versions of the Grothendieck-Riemann-Roch theorem that would allow for the calculation of torsion information.(C) He is studying the representations that appear in the cohomology of arithmetic varieties with a finite group action.In particular, he continues his work on developing fixed point formulas for calculating invariants of such (integral) representations using two interconnected themes: the theory of cubic structures and the theory of central extensions of algebraic loop groups.The investigator's research is in the field of arithmetic algebraic geometry, a subject that blends two of the oldest areas of mathematics: the geometry of figures that can be defined by the simplest equations, namely polynomials, and the study of numbers. This combination has proved extraordinarily fruitful - having solved problems that withstood generations (such as ``Fermat's last theorem"). The investigator's work mainly concentrates on the study of certain polynomial equations that have many symmetries. There are connections with physics, the construction of error correcting codes and cryptography.
主要研究者正在研究以下三个问题:(A)他试图描述Shimura簇在非光滑约化素数下的积分模型。特别是,他研究“本地模型”, 志村簇及其与无限维群的仿射旗簇和伽罗瓦表示的变形空间的关系。其动机是为了获得信息,可以用于计算这些品种的Hasse-Weil zeta函数和其他数论应用。(B)他正在开发精细和函子版本的格罗滕迪克-黎曼-罗克定理,这将允许计算扭转信息。(C)他正在研究出现在有限群作用的算术变种的上同调中的表示。特别是,他继续他的工作,发展不动点公式,用于计算这样的不变量。(积分)表示使用两个相互关联的主题:立方结构理论和代数圈群的中心扩展理论。研究者的研究领域是算术代数几何,一门融合了两个最古老的数学领域的学科:可以由最简单的方程(即多项式)定义的图形几何学和对数字的研究。这种结合已经证明是非常富有成效的-解决了几代人的问题(如“费马最后定理”)。研究者的工作主要集中在研究某些具有许多对称性的多项式方程。这与物理学、纠错码的构造和密码学有关。
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)
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Georgios Pappas其他文献
ЯКІСТЬ ВИЩОЇ ОСВІТИ ТА ЕКСПЕРТНИЙ СУПРОВІД ЇЇ ЗАБЕЗПЕЧЕННЯ: ДОСВІД ЄС QUALITY ASSURANCE IN HIGHER EDUCATION AND ITS EXPERT SUPPORT: THE EU EXPERIENCE
高等教育质量保证国家及其专家支持:欧盟的经验
- DOI:
- 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Georgios Pappas - 通讯作者:
Georgios Pappas
The physical and biogeochemical parameters along the coastal waters of Saudi Arabia during field surveys in summer, 2021
2021年夏季实地调查沙特阿拉伯沿海水域物理和生物地球化学参数
- DOI:
10.5194/essd-16-1703-2024 - 发表时间:
2024 - 期刊:
- 影响因子:11.4
- 作者:
Y. Abualnaja;A. Pavlidou;James H. Churchill;Ioannis Hatzianestis;D. Velaoras;H. Kontoyiannis;V. Papadopoulos;A. Karageorgis;Georgia Assimakopoulou;H. Kaberi;Theodoros Kannelopoulos;C. Parinos;C. Zeri;Dionysios Ballas;Elli Pitta;V. Paraskevopoulou;Afroditi Androni;S. Chourdaki;Vassileia Fioraki;S. Iliakis;Georgia Kabouri;Angeliki Konstantinopoulou;G. Krokos;D. Papageorgiou;Alkiviadis Papageorgiou;Georgios Pappas;E. Plakidi;E. Rousselaki;Ioanna Stavrakaki;E. Tzempelikou;P. Zachioti;A. Yfanti;Theodore Zoulias;Abdulah Al Amoudi;Yasser Alshehri;Ahmad Alharbi;Hammad Al Sulami;Taha Boksmati;Rayan Mutwalli;I. Hoteit - 通讯作者:
I. Hoteit
Existing tools used in the framework of environmental performance
环境绩效框架中使用的现有工具
- DOI:
10.1016/j.scp.2023.101026 - 发表时间:
2023 - 期刊:
- 影响因子:6
- 作者:
I. Papamichael;I. Voukkali;P. Loizia;Georgios Pappas;A. Zorpas - 通讯作者:
A. Zorpas
Horizontal gene transfer confers fermentative metabolism in the respiratory-deficient plant trypanosomatid <em>Phytomonas serpens</em>
- DOI:
10.1016/j.meegid.2012.01.016 - 发表时间:
2012-04-01 - 期刊:
- 影响因子:
- 作者:
Susan Ienne;Georgios Pappas;Karim Benabdellah;Antonio González;Bianca Zingales - 通讯作者:
Bianca Zingales
Horton’s three sisters: familial clustering of temporal arteritis
- DOI:
10.1007/s10067-007-0610-5 - 发表时间:
2007-03-27 - 期刊:
- 影响因子:2.800
- 作者:
Lampros Raptis;Georgios Pappas;Nikolaos Akritidis - 通讯作者:
Nikolaos Akritidis
Georgios Pappas的其他文献
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{{ truncateString('Georgios Pappas', 18)}}的其他基金
Shimura Varieties, p-Adic Shtukas, and Local Systems
志村品种、p-Adic Shtukas 和本地系统
- 批准号:
2100743 - 财政年份:2021
- 资助金额:
$ 15万 - 项目类别:
Standard Grant
Arithmetic Geometry: Shimura Varieties, Galois Modules, and Iwasawa Theory
算术几何:志村簇、伽罗瓦模和岩泽理论
- 批准号:
1701619 - 财政年份:2017
- 资助金额:
$ 15万 - 项目类别:
Standard Grant
FRG: Collaborative Research: Chern classes in Iwasawa Theory
FRG:合作研究:岩泽理论中的陈省身课程
- 批准号:
1360733 - 财政年份:2014
- 资助金额:
$ 15万 - 项目类别:
Continuing Grant
Shimura varieties, Galois modules and Galois representations
Shimura 簇、伽罗瓦模和伽罗瓦表示
- 批准号:
1102208 - 财政年份:2011
- 资助金额:
$ 15万 - 项目类别:
Continuing Grant
Shimura Varieties and Galois Modules
Shimura 簇和伽罗瓦模块
- 批准号:
0501049 - 财政年份:2005
- 资助金额:
$ 15万 - 项目类别:
Standard Grant
Shimura Varieties, Galois Modules and the Determinant of Cohomology
Shimura 簇、伽罗瓦模和上同调行列式
- 批准号:
0201140 - 财政年份:2002
- 资助金额:
$ 15万 - 项目类别:
Continuing Grant
Shimura Varieties, Galois Modules and L-functions
Shimura 簇、伽罗瓦模块和 L 函数
- 批准号:
9970378 - 财政年份:1999
- 资助金额:
$ 15万 - 项目类别:
Standard Grant
Mathematical Sciences: Arithmetic Models for Shimura Varieties, L-Functions and Cohomology Groups as Integral Representations
数学科学:Shimura 簇、L 函数和上同调群的算术模型作为积分表示
- 批准号:
9996393 - 财政年份:1999
- 资助金额:
$ 15万 - 项目类别:
Continuing Grant
Mathematical Sciences: Arithmetic Models for Shimura Varieties, L-Functions and Cohomology Groups as Integral Representations
数学科学:Shimura 簇、L 函数和上同调群的算术模型作为积分表示
- 批准号:
9623269 - 财政年份:1996
- 资助金额:
$ 15万 - 项目类别:
Continuing Grant
Mathematical Sciences: Models for Hilbert Varieties and Galois Structure of deRham Cohomology
数学科学:希尔伯特簇模型和 deRham 上同调的伽罗瓦结构
- 批准号:
9596104 - 财政年份:1994
- 资助金额:
$ 15万 - 项目类别:
Continuing Grant
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