Variation of Selmer Groups

Selmer 群的变体

• 批准号: 0400232
• 负责人: Ravi Ramakrishna
• 金额: $ 15万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2004
• 资助国家: 美国
• 起止时间: 2004-07-01 至 2008-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0400232&HistoricalAwards=false
• 关键词: Variation; Selmer; Groups

Abstract for award DMS-0400232 of Ramakrishna: The main purpose of this project is to continue aninvestigation of the PI of mod p Galois representations,p-adic Galois representations and their relations withproblems in number theory and arithmetic algebraic geometry.A particular emphasis will be the understanding of how Selmergroups of various sorts change as more primes are addedto the ramification set. In one context this variationof Selmer groups relates to how many `new at q' newforms there arecongruent to a particular oldform. The PI's research is in Algebraic Number Theory.This field has its roots in the study of whole numbers and theirvarious properties. A key tool in the PI's researchis Galois theory. Galois theory is the study of symmetries of solutionsof equations. The understanding of these symmetriesshed slight on the the solutions themselves, abasic mathematical question. An example of such a symmetry is thefact that complex solutions to polynomial equations occur incomplex conjugate pairs.

Ramakrishna的DMS-0400232奖项摘要： 本项目的主要目的是继续研究模p伽罗瓦表示、p-adic伽罗瓦表示的PI以及它们与数论和算术代数几何中问题的关系，特别强调理解各种Selmer群如何随着更多的素数被添加到分支集而变化。在一个上下文中，塞尔默群的这种变化与有多少“在q处新"的新形式全等于一个特定的旧形式有关。 PI的研究方向是代数数论，这一领域的根基在于研究整数及其各种性质。PI研究的一个关键工具是伽罗瓦理论。伽罗瓦理论是研究方程解的对称性的理论。对这些对称性的理解忽视了解本身这一基本数学问题。这种对称性的一个例子是多项式方程的复解出现在复共轭对中。