Rational points on algebric varieties

代数簇的有理点

• 批准号: 250196-2007
• 负责人: McKinnon, David
• 金额: $ 1.09万
• 依托单位: University of Waterloo
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2010
• 资助国家: 加拿大
• 起止时间: 2010-01-01 至 2011-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=455601
• 关键词: Rational; points; algebric; varieties

One of the fundamental goals of number theory is to find solutions in whole numbers to certain kinds of equations called Diophantine equations. These equations can often be interpreted in a geometric manner, and therefore geometric techniques can be brought to bear on the solution of the problem. Paul Vojta has made some wide-ranging conjectures on what kinds of solutions Diophantine equations should have, based on what kind of geometrical properties the equations have. In my future research, I propose to study these conjectures, try to improve on my previous proofs of various special cases of them, and try to use existing results to gain further insight into the solutions of Diophantine equations.

数论的基本目标之一是找到某些称为丢番图方程的方程的整数解。 这些方程通常可以用几何方式解释，因此可以利用几何技术来解决问题。保罗·沃伊塔（Paul Vojta）根据丢番图方程具有什么样的几何性质，对丢番图方程应该有什么样的解做出了一些广泛的猜想。 在我未来的研究中，我建议研究这些猜想，尝试改进我之前对它们的各种特殊情况的证明，并尝试使用现有的结果来进一步了解丢番图方程的解。