POWRE: Abelian Varieties and Shimura Varieties

POWRE：阿贝尔品种和志村品种

• 批准号: 9805854
• 负责人: Alice Silverberg
• 金额: $ 4.62万
• 依托单位: University of California-Berkeley
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1998
• 资助国家: 美国
• 起止时间: 1998-08-15 至 2000-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9805854&HistoricalAwards=false
• 关键词: POWRE; Abelian; Varieties; Shimura

Silverberg 9805854 The research is in the fields of Number Theory and Arithmetic Algebraic Geometry, with a focus on abelian varieties and Shimura varieties. The questions to be studied concern f-adic representations, adelic representations, ranks of elliptic curves, fields of definition, fields of moduli, and torsion points on abelian varieties. Silverberg will use a POWRE grant to be a Visiting Professor at the University of California at Berkeley. This will contribute positively to her research, career advancement, visibility, and professional growth. Abelian varieties and Shimura varieties are important mathematical objects which arise in a wide variety of areas, and were used in Faltings' proof of the Mordell Conjecture and in Wiles' proof of the Semistable ShimuraTaniyama Conjecture. Arithmetic Algebraic Geometry is a subject that blends two of the oldest areas of Mathematics: Number Theory and Algebraic Geometry. This combination has proved extraordinarily fruitful, having recently solved problems that withstood generations. Among the many applications are new error correcting codes. Such codes are essential for both modern computers (hard disks) and compact disks. Number Theory and Algebraic Geometry have found numerous applications in data transmission and processing, communication systems, physics, theoretical computer science, and robotics.

Silverberg 9805854该研究是在数论和算术代数几何领域，重点是阿贝尔品种和志村品种。要研究的问题涉及f-进表示，adelic表示，行列的椭圆曲线，领域的定义，领域的模，和扭点的交换品种。 西尔弗伯格将使用POWRE赠款是一个访问教授在加州大学伯克利分校。这将有助于她的研究，职业发展，知名度和专业成长。 阿贝尔簇和志村簇是重要的数学对象，它们出现在广泛的领域，并被用于法尔丁斯的莫德尔猜想的证明和怀尔斯的半稳定志村谷山猜想的证明。算术代数几何是一个融合了数学的两个最古老的领域：数论和代数几何的主题。事实证明，这种结合非常富有成效，最近解决了几代人面临的问题。在众多应用中，有新的纠错码。这种代码对于现代计算机（硬盘）和光盘都是必不可少的。数论和代数几何在数据传输和处理、通信系统、物理学、理论计算机科学和机器人技术中有许多应用。