Mathematical Sciences: The Integral Hecke Structure of Shimura Curves

数学科学：志村曲线的积分赫克结构

• 批准号: 8709522
• 负责人: Bruce Jordan
• 金额: $ 3.86万
• 依托单位: CUNY Baruch College
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1987
• 资助国家: 美国
• 起止时间: 1987-07-01 至 1989-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=8709522&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Integral; Hecke; Structure

This research concerns the Shimura curve associated to an indefinite rational quaternion division algebra. The rational structure of these curves have been understood for a long time, however there are many important questions to be answered concerning their integral structure. Drinfeld gave the description as a course moduli scheme and this research will investigate their Hecke structure. This research is in one of the most erudite areas of arithmetic algebraic geometry, that subject which blends algebraic and geometric (and in this case analytic) techniques to answer questions in number theory. This research has already been a crucial ingredient in solving one of the big problems settled this year and will continue in the same direction during the tenure of this award. Much of great interest will be accomplished.

本文研究了与不定有理四元数除法代数相关的志村曲线。这些曲线的合理结构早已为人所知，但其整体结构仍有许多重要问题有待解答。Drinfeld将其描述为一种课程模方案，本研究将探讨它们的Hecke结构。这项研究是算术代数几何中最博学的领域之一，这个学科融合了代数和几何（在这种情况下是解析）技术来回答数论中的问题。这项研究已经成为解决今年解决的一个重大问题的关键因素，并将在本奖项的任期内继续朝着相同的方向发展。许多有趣的事情将会完成。