CLASS INVARIANTS FOR ABELIAN VARIETIES OF HIGHER DIMENSION

高维阿贝尔簇的类不变量

• 批准号: EP/D066816/1
• 负责人: Jean Gillibert
• 金额: $ 22.75万
• 依托单位: University of Manchester
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2006
• 资助国家: 英国
• 起止时间: 2006 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FD066816%2F1
• 关键词: CLASS; INVARIANTS; ABELIAN; VARIETIES; HIGHER

The principal subject of this research project is geometric Galois structure . Galois structure appeared first in number theory, and has motivated research of many people. This subject was later extended in the context of arithmetic algebraic geometry. More precisely, Martin Taylor has stated in 1988 a conjecture which says that certain Galois structure invariants attached to elliptic curves, should vanish. This has been established by Taylor and others. Now, my aim is to obtain positive results on (an analogue of) Taylor's conjecture for abelian varieties of higher dimension.Taylor's conjecture is stated in the context of varieties having everywhere good reduction. A natural question to ask is : what does happens in the bad reduction case ? In my PhD, I have shown how Taylor's conjecture can be generalized to semi-stable abelian varieties. Also, I have proven that the vanishing result was still true, in some extent, for semi-stable elliptic curves. As the semi-stable case is much more frequent than the good reduction case, this enlarges the field of investigations. In this context, counter-examples to Taylor's conjecture can be expected to be found.This project can establish collaboration with researchers abroad (from countries like Germany, France and the US).AMS MSC code : 11Gxx, 11Rxx, 14Kxx

本课题的主要研究对象是几何伽罗瓦结构。伽罗瓦结构最早出现在数论中，并激发了许多人的研究。这一主题后来在算术代数几何的范围内得到扩展。更确切地说，马丁·泰勒在1988年提出了一个猜想，即某些附加在椭圆曲线上的伽罗瓦结构不变量应该消失。这是泰勒和其他人提出的。现在，我的目标是获得积极的结果（模拟）泰勒猜想的阿贝尔品种的高维。泰勒猜想的背景下，品种有无处不在的良好减少。一个很自然的问题是：在坏的还原情况下会发生什么？在我的博士学位，我已经表明如何泰勒的猜想可以推广到半稳定的阿贝尔品种。同时，证明了对于半稳定椭圆曲线，消失结果在一定程度上仍然成立。由于半稳定的情况比良好的情况更频繁，这扩大了调查的领域。在此背景下，有望找到泰勒猜想的反例。该项目可以与国外的研究人员（来自德国，法国和美国等国家）建立合作。AMS MSC代码：11Gxx，11Rxx，14Kxx

项目成果

Invariants de classes : exemples de non-annulation en dimension supérieure

类的不变量：上维非循环的例子

• DOI: 10.1007/s00208-007-0084-4
• 发表时间: 2007
• 期刊: Mathematische Annalen
• 影响因子: 1.4
• 作者: Gillibert J