"Hurwitz spaces, Humbert schemes and modular curves"

“赫尔维茨空间、亨伯特方案和模曲线”

• 批准号: 105361-2012
• 负责人: Kani, Ernst
• 金额: $ 0.87万
• 依托单位: Queen's University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=593205
• 关键词: Hurwitz; spaces; Humbert; schemes; modular

This research program belongs mainly to the area of arithmetic geometry, i.e., to the area which applies the methods of algebraic geometry to solve problems in number theory. A typical example here is the famous Fermat equation x^n + y^n = z^n, where n > 2. Fermat asserted in 1640 that this equation has no solution in positive integers, i.e., that the sum of two n-th powers can never be an n-th power, if n > 2. This was resolved in 1995 when Wiles, using ideas and results of Frey and Ribet in arithmetic geometry, proved that this assertion is indeed true.

这项研究计划主要属于算术几何领域，即，应用代数几何方法解决数论问题的领域。一个典型的例子是著名的费马方程x^n + y^n = z^n，其中n > 2。费马在1640年断言，这个方程在正整数中没有解，即，如果n > 2，两个n次方的和永远不会是n次方。这是解决在1995年时，怀尔斯，使用的想法和成果弗雷和里贝特在算术几何，证明了这一主张确实是正确的。