Mathematical Sciences: Arithmetic of Automorphic Forms on Certain Shimura Varieties

数学科学：某些志村品种的自守形式的算术

• 批准号: 9001878
• 负责人: Don Blasius
• 金额: $ 10.43万
• 依托单位: University of California-Los Angeles
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-05-01 至 1994-04-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001878&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Arithmetic; Automorphic; Forms

This award supports the research in automorphic forms of Professor Don Blasius of the University of California at Los Angeles. Dr. Blasius's project is to complete the construction of Galois representations for Maass forms of Galois type by extending to coherent cohomology certain methods of interpre- tation that have been established for holomorphic forms; to stabilize the Trace Formula for GSp(4), beginning with the Fundamental Lemma; and to study certain lifting problems involving Abelian varieties, in the setting of Shimura varieties, applying his work on p-adic properties of Hodge classes. Non-Euclidean plane geometry began in the early nineteenth century as a mathematical curiosity, but by the end of that century, mathematicians had realized that many objects of fundamental importance are non-Euclidean in their basic nature. The detailed study of non-Euclidean plane geometries has given rise to several branches of modern mathematics, of which the study of modular and automorphic forms is one of the most active. This field is principally concerned with questions about the whole numbers, but in its use of geometry and analysis, it retains connection to its historical roots.

该奖项支持加州大学洛杉矶分校的唐·布拉修斯教授进行的自同构形式的研究。Blasius博士的项目是通过将已建立的全纯形式的某些解释方法推广到凝聚上同调来完成Galois类型Maas型形式的Galois表示的构造：从基本引理开始，稳定GSP(4)的迹公式；在Shimura簇的背景下，应用他关于Hodge类的p-进性质的工作，研究了涉及Abelian簇的某些提升问题。非欧几里得平面几何始于十九世纪初，最初是一种数学奇闻，但到那个世纪末，数学家们已经意识到许多具有根本重要性的物体本质上都是非欧几里得的。对非欧几里得平面几何的详细研究已经产生了现代数学的几个分支，其中模和自同构形的研究是最活跃的之一。这一领域主要涉及关于整数的问题，但在几何和分析的使用中，它保留了与其历史根源的联系。