Refining the Chabauty--Coleman method for modular curves
改进模曲线的 Chabauty--Coleman 方法
基本信息
- 批准号:2441146
- 负责人:
- 金额:--
- 依托单位:
- 依托单位国家:英国
- 项目类别:Studentship
- 财政年份:2020
- 资助国家:英国
- 起止时间:2020 至 无数据
- 项目状态:未结题
- 来源:
- 关键词:
项目摘要
Robin Visser's PhD project lies in the area of number theory, developing techniques to bound the number of rational solutions to a given equation. In particular, he will focus on finding upper bounds for the number of points on modular curves (certain specific algebraic curves related to the arithmetic of modular forms) which are defined over number fields of small degree. This problem has recently been intensively studied by Siksek, Visser's proposed supervisor, motivated by applications to modularity problems for elliptic curves over totally-real quadratic and cubic fields. Siksek used a classical technique due to Chabauty and Coleman to find all rational points on the d-th symmetric power of the curve for small d, which is equivalent to finding all points on the original curve over all degree d number fields simultaneously. At present, the bounds onthe set of solutions given by Chabauty--Coleman are far from optimal, which poses difficulties in applying this method to concrete problems arising in modularity theory. The goal of Visser's project is to refine the Chabauty-- Coleman method for modular curves by making use of the fact that the system of equations that arises is heavily over-determined, a property which has not been systematically exploited in previous work. This should allow much more precise bounds to be obtained, greatly strengthening the potential applications of the method to modularity of elliptic curves and other classical problems. This project addresses the EPSRC research area "Number theory", within the"Mathematical Sciences" theme.
Robin Visser的博士项目位于数论领域,开发了将有理解的数量限制在给定方程的数量的技术。特别是,他将专注于寻找定义在小次数数域上的模曲线(与模形式的算术相关的某些特定代数曲线)上的点数的上界。最近,Visser推荐的主管Siksek对这个问题进行了深入的研究,其动机是将其应用于全实二次和三次域上椭圆曲线的模性问题。Siksek利用Chabauty和Coleman提出的一种经典方法求出了小d的曲线的d次对称幂上的所有有理点,这相当于同时求出所有d次数域上原曲线上的所有点。目前,Chabauty-Coleman给出的解集的界远不是最优的,这给将这种方法应用于模块化理论中的具体问题带来了困难。Visser项目的目标是通过利用所产生的方程组严重超定的事实来改进模曲线的Chabauty-Coleman方法,这一特性在以前的工作中没有被系统地利用。这应该允许获得更精确的界,极大地加强了该方法在椭圆曲线的模性和其他经典问题中的潜在应用。本项目以“数学科学”为主题,探讨EPSRC的研究领域“数论”。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
数据更新时间:{{ journalArticles.updateTime }}
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
数据更新时间:{{ journalArticles.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ monograph.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ sciAawards.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ conferencePapers.updateTime }}
{{ item.title }}
- 作者:
{{ item.author }}
数据更新时间:{{ patent.updateTime }}
其他文献
Internet-administered, low-intensity cognitive behavioral therapy for parents of children treated for cancer: A feasibility trial (ENGAGE).
针对癌症儿童父母的互联网管理、低强度认知行为疗法:可行性试验 (ENGAGE)。
- DOI:
10.1002/cam4.5377 - 发表时间:
2023-03 - 期刊:
- 影响因子:4
- 作者:
- 通讯作者:
Differences in child and adolescent exposure to unhealthy food and beverage advertising on television in a self-regulatory environment.
在自我监管的环境中,儿童和青少年在电视上接触不健康食品和饮料广告的情况存在差异。
- DOI:
10.1186/s12889-023-15027-w - 发表时间:
2023-03-23 - 期刊:
- 影响因子:4.5
- 作者:
- 通讯作者:
The association between rheumatoid arthritis and reduced estimated cardiorespiratory fitness is mediated by physical symptoms and negative emotions: a cross-sectional study.
类风湿性关节炎与估计心肺健康降低之间的关联是由身体症状和负面情绪介导的:一项横断面研究。
- DOI:
10.1007/s10067-023-06584-x - 发表时间:
2023-07 - 期刊:
- 影响因子:3.4
- 作者:
- 通讯作者:
ElasticBLAST: accelerating sequence search via cloud computing.
ElasticBLAST:通过云计算加速序列搜索。
- DOI:
10.1186/s12859-023-05245-9 - 发表时间:
2023-03-26 - 期刊:
- 影响因子:3
- 作者:
- 通讯作者:
Amplified EQCM-D detection of extracellular vesicles using 2D gold nanostructured arrays fabricated by block copolymer self-assembly.
使用通过嵌段共聚物自组装制造的 2D 金纳米结构阵列放大 EQCM-D 检测细胞外囊泡。
- DOI:
10.1039/d2nh00424k - 发表时间:
2023-03-27 - 期刊:
- 影响因子:9.7
- 作者:
- 通讯作者:
的其他文献
{{
item.title }}
{{ item.translation_title }}
- DOI:
{{ item.doi }} - 发表时间:
{{ item.publish_year }} - 期刊:
- 影响因子:{{ item.factor }}
- 作者:
{{ item.authors }} - 通讯作者:
{{ item.author }}
{{ truncateString('', 18)}}的其他基金
An implantable biosensor microsystem for real-time measurement of circulating biomarkers
用于实时测量循环生物标志物的植入式生物传感器微系统
- 批准号:
2901954 - 财政年份:2028
- 资助金额:
-- - 项目类别:
Studentship
Exploiting the polysaccharide breakdown capacity of the human gut microbiome to develop environmentally sustainable dishwashing solutions
利用人类肠道微生物群的多糖分解能力来开发环境可持续的洗碗解决方案
- 批准号:
2896097 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
A Robot that Swims Through Granular Materials
可以在颗粒材料中游动的机器人
- 批准号:
2780268 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Likelihood and impact of severe space weather events on the resilience of nuclear power and safeguards monitoring.
严重空间天气事件对核电和保障监督的恢复力的可能性和影响。
- 批准号:
2908918 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Proton, alpha and gamma irradiation assisted stress corrosion cracking: understanding the fuel-stainless steel interface
质子、α 和 γ 辐照辅助应力腐蚀开裂:了解燃料-不锈钢界面
- 批准号:
2908693 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Field Assisted Sintering of Nuclear Fuel Simulants
核燃料模拟物的现场辅助烧结
- 批准号:
2908917 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Assessment of new fatigue capable titanium alloys for aerospace applications
评估用于航空航天应用的新型抗疲劳钛合金
- 批准号:
2879438 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Developing a 3D printed skin model using a Dextran - Collagen hydrogel to analyse the cellular and epigenetic effects of interleukin-17 inhibitors in
使用右旋糖酐-胶原蛋白水凝胶开发 3D 打印皮肤模型,以分析白细胞介素 17 抑制剂的细胞和表观遗传效应
- 批准号:
2890513 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
Understanding the interplay between the gut microbiome, behavior and urbanisation in wild birds
了解野生鸟类肠道微生物组、行为和城市化之间的相互作用
- 批准号:
2876993 - 财政年份:2027
- 资助金额:
-- - 项目类别:
Studentship
相似海外基金
Quadratic Chabauty for integral points
积分点的二次 Chabauty
- 批准号:
325713478 - 财政年份:2016
- 资助金额:
-- - 项目类别:
Research Grants
Explicit Chabauty-Kim theory for the thrice punctured line
三次穿刺线的显式 Chabauty-Kim 理论
- 批准号:
239470564 - 财政年份:2013
- 资助金额:
-- - 项目类别:
Priority Programmes
Applications of chabauty`s method
查博蒂方法的应用
- 批准号:
367234-2008 - 财政年份:2008
- 资助金额:
-- - 项目类别:
University Undergraduate Student Research Awards
Mathematical Sciences: The Method of Coleman and Chabauty
数学科学:科尔曼和查博蒂的方法
- 批准号:
9624219 - 财政年份:1996
- 资助金额:
-- - 项目类别:
Standard Grant














{{item.name}}会员




