Anabelian Geometry and Field Arithmetic

阿纳贝尔几何和场算术

基本信息

  • 批准号:
    0801144
  • 负责人:
  • 金额:
    $ 15万
  • 依托单位:
  • 依托单位国家:
    美国
  • 项目类别:
    Continuing Grant
  • 财政年份:
    2008
  • 资助国家:
    美国
  • 起止时间:
    2008-07-15 至 2011-10-31
  • 项目状态:
    已结题

项目摘要

The Principal Investigator plans to continue his study of Anabelian geometry and of Field Arithmetic, as well as the interaction of these two subjects with other aspects of mathematics in general, and with arithmetic geometry and algebraic geometry in particular.This study will be guided in part by possible extensions of the known anabelian phenomena, and of the known facts from field arithmetic, to which the PI has made major contributions. The PI expects to prove the pro-l abelian-by-central birational anabelian Conjecture for function fields of tr.degree 1 over algebraic closures of finite fields, of global fields, and even more general algebraically closed fields. The PI expects to obtain the pro-l abelian-by-central form of the Ihara/Oda--Matsumoto conjecture, which would have a major impact on understanding the Galois structure of the field of rational numbers (and other fields). The PI expects as well to make progress on Grothendieck's (p-adic) Section Conjecture and its relation to (an effective) Mordell Conjecture --Faltings' Theorem. The PI expects to make progress on better understanding the class of large fields, and of the cohomology of fields as related to the Freeness Conjecture.Positive answers to the questions mentioned above would have a very significant impact on the progress of modern Galois theory, and on some of the very fundamental questions in arithmetic geometry and algebraic geometry. The results will be widely disseminated to the mathematical community via talks and publications in scientific journals. The PI is co-organizer of, and senior invited researcher at, activities which plan to do both: first, to create a broad basis for international cooperation, training, and scientific exchange at all levels, and second, to have special activities for graduate students and young researchers, thus enhancing teaching and technological understanding.
首席研究员计划继续他的研究Anabelian几何和领域算术,以及这两个主题的相互作用与其他方面的数学一般,并与算术几何和代数几何特别是。这项研究将部分指导可能的扩展已知的anabelian现象,并从领域算术已知的事实,其中PI作出了重大贡献。PI期望证明tr.degree 1的函数域在有限域、全局域以及更一般的代数闭域的代数闭包上的pro-l阿贝尔-中心双有理anabelian猜想。PI期望获得Ihara/Oda-松本猜想的中心形式,这将对理解有理数领域(和其他领域)的伽罗瓦结构产生重大影响。PI也期望在Grothendieck的(p-adic)截面猜想及其与(一个有效的)Mordell猜想--Faltings定理的关系上取得进展。PI期望在更好地理解大场类以及与Freeness猜想相关的场的上同调方面取得进展。对上述问题的肯定回答将对现代伽罗瓦理论的进展以及算术几何和代数几何中的一些非常基本的问题产生非常重要的影响。研究结果将通过讲座和科学期刊上的出版物广泛传播给数学界。PI是共同组织者和高级特邀研究员,这些活动计划做到两点:第一,为各级国际合作,培训和科学交流创造广泛的基础,第二,为研究生和年轻研究人员举办特别活动,从而提高教学和技术理解。

项目成果

期刊论文数量(0)
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会议论文数量(0)
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Florian Pop其他文献

On prosolvable subgroups of profinite free products and some applications
  • DOI:
    10.1007/bf02567982
  • 发表时间:
    1995-12-01
  • 期刊:
  • 影响因子:
    0.600
  • 作者:
    Florian Pop
  • 通讯作者:
    Florian Pop
Galoissche Kennzeichnung p-adisch abgeschlossener Körper.
Galoissche Kennzeichnung p-adisch abgeschlossener Körper。
On the Pythagoras number of function fields of curves over number fields
  • DOI:
    10.1007/s11856-023-2548-y
  • 发表时间:
    2023-12-22
  • 期刊:
  • 影响因子:
    0.800
  • 作者:
    Florian Pop
  • 通讯作者:
    Florian Pop
Elementary equivalence versus isomorphism
  • DOI:
    10.1007/s00222-002-0238-7
  • 发表时间:
    2002-11-01
  • 期刊:
  • 影响因子:
    3.600
  • 作者:
    Florian Pop
  • 通讯作者:
    Florian Pop
Pro-ℓ abelian-by-central Galois theory of prime divisors
  • DOI:
    10.1007/s11856-010-0093-y
  • 发表时间:
    2010-10-31
  • 期刊:
  • 影响因子:
    0.800
  • 作者:
    Florian Pop
  • 通讯作者:
    Florian Pop

Florian Pop的其他文献

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{{ truncateString('Florian Pop', 18)}}的其他基金

FRG: Collaborative Research: Definability and Computability over Arithmetically Significant Fields
FRG:协作研究:算术上重要字段的可定义性和可计算性
  • 批准号:
    2152304
  • 财政年份:
    2022
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Anabelian Geometry and Field Arithmetic II
阿纳贝尔几何与域算术 II
  • 批准号:
    1101397
  • 财政年份:
    2011
  • 资助金额:
    $ 15万
  • 项目类别:
    Continuing Grant
Travel Funding for Workshop at RIMS Kyoto
RIMS 京都研讨会旅行资助
  • 批准号:
    1044746
  • 财政年份:
    2010
  • 资助金额:
    $ 15万
  • 项目类别:
    Standard Grant
Anabelian Geometry and Elementary Equivalence of Fields
阿纳贝尔几何和域的初等等价
  • 批准号:
    0401056
  • 财政年份:
    2004
  • 资助金额:
    $ 15万
  • 项目类别:
    Continuing Grant

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