Adic Modular Forms

Adic 模块化形式

基本信息

  • 批准号:
    RGPIN-2016-06731
  • 负责人:
  • 金额:
    $ 3.35万
  • 依托单位:
  • 依托单位国家:
    加拿大
  • 项目类别:
    Discovery Grants Program - Individual
  • 财政年份:
    2019
  • 资助国家:
    加拿大
  • 起止时间:
    2019-01-01 至 2020-12-31
  • 项目状态:
    已结题

项目摘要

The research projects that I would like to propose are projects in the field of Number Theory. Number Theory is one of the oldest branches of Mathematics, its origins in the Western civilization can be traced back to antiquity. Its main object of study is the set of integer numbers which were seen by the disciples of the Pythagorean school as magical carrying in mysterious ways all the information in existence.***After two thousand years if intense study the set of integer numbers is still mysterious and very attractive for human enquiry. During the seventeenth century (AD 1637) Pierre de Fermat started investigating the integer solutions of the family of equations X^N+Y^N=Z^N, for N=3,4,5,.... This study is known as ``Fermat's last theorem" and it states that: there are no non-zero integer solutions to the equations X^N+Y^N=Z^N, for N=3,4,5,...***Fermat thought he proved the theorem but did not write the solution. Attempts to recover Fermat's solution (assuming it ever existed)***or to otherwise substantiate his claims spawned the birth of new Mathematical theories to which many great mathematicians contributed in profound ways culminating with Andrew Wiles' first published proof of the Theorem in 1995. Wiles' proof of Fermat's last theorem parlays a non-trivial solution of the ***equation X^p+Y^p=Z^p into the construction of an elliptic curve which can be then shown to posses an unlikely assortment of properties; he was then able to ***show that such an elliptic curve cannot exist by exploiting a deep, far reaching and still largely unproved connection between the various algebraic structures that arise from ``modular forms". Their role in our subject is fundamental and they, modular forms that is, are also the main characters of my own research. More precisely I am interested in understanding the $p$-adic properties of modular forms. Having fixed a prime integer p, i.e. any integer from the (infinite) list: 2,3,5,7,11,13,17,19,23,... it is interesting to study the divisibility of various integers by powers of p and this can be seen as defining a ``new distance" on the set of integers: namely two integers are ``near" if their***difference is divisible by a high power of p. In this funny distance, called p-adic distance, there are many gaps between various integers and if we fill in all these gaps, we obtain a much larger set (ring)&n
我要提出的研究项目是数论领域的项目。数论是数学中最古老的分支之一,它起源于西方文明,可以追溯到古代。它的主要研究对象是整数集,它被毕达哥拉斯学派的信徒视为神奇地以神秘的方式承载着所有存在的信息。*经过两千年的密集研究,整数集仍然神秘,非常吸引人类的探究。在17世纪(公元1637年),皮埃尔·德·费马开始研究方程X^N+Y^N=Z^N的整数解,其中N=3,4,5,……这项研究被称为‘费马最后定理’,它指出:方程X^N+Y^N=Z^N不存在非零整数解,对于N=3,4,5,……*费马认为他证明了这个定理,但没有写出解。试图恢复费马的解(假设它曾经存在)*或以其他方式证实他的主张催生了新的数学理论,许多伟大的数学家以深刻的方式对此做出了贡献,安德鲁·怀尔斯于1995年首次发表了《定理的证明》。Wiles对Fermat最后定理的证明将*方程X^p+Y^p=Z^p的非平凡解应用到椭圆曲线的构造中,然后可以证明该椭圆曲线具有不太可能的各种性质;然后,他能够*证明这样一条椭圆曲线不可能存在,这是通过利用从‘模形式’产生的各种代数结构之间的深刻、深远且在很大程度上仍未得到证明的联系来实现的。它们在我们的学科中的作用是基本的,它们,也就是模块形式,也是我自己研究的主要特征。更确切地说,我感兴趣的是了解模形式的$p$-进的性质。有固定的素数p,即(无限)列表中的任何整数:2,3,5,7,11,13,17,19,23,...研究各种整数的p次方可整除性是很有趣的,这可以被看作是在整数集合上定义了一种新的距离:即,如果两个整数的*差可以被p的高次幂整除,则两个整数是“接近”的。在这个有趣的距离中,各种整数之间有许多空位,如果我们填满所有这些空位,我们得到一个更大的集合(环)&n

项目成果

期刊论文数量(0)
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Iovita, Adrian其他文献

p-adic families of Siegel modular cuspforms
  • DOI:
    10.4007/annals.2015.181.2.5
  • 发表时间:
    2015-03-01
  • 期刊:
  • 影响因子:
    4.9
  • 作者:
    Andreatta, Fabrizio;Iovita, Adrian;Pilloni, Vincent
  • 通讯作者:
    Pilloni, Vincent

Iovita, Adrian的其他文献

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{{ truncateString('Iovita, Adrian', 18)}}的其他基金

p-Adic variation of motives
动机的 p-Adic 变化
  • 批准号:
    RGPIN-2022-04711
  • 财政年份:
    2022
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Adic Modular Forms
Adic 模块化形式
  • 批准号:
    RGPIN-2016-06731
  • 财政年份:
    2021
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Adic Modular Forms
Adic 模块化形式
  • 批准号:
    RGPIN-2016-06731
  • 财政年份:
    2020
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Adic Modular Forms
Adic 模块化形式
  • 批准号:
    RGPIN-2016-06731
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Adic Modular Forms
Adic 模块化形式
  • 批准号:
    RGPIN-2016-06731
  • 财政年份:
    2017
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Adic Modular Forms
Adic 模块化形式
  • 批准号:
    RGPIN-2016-06731
  • 财政年份:
    2016
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Comparison isomorphisms and arithmetic applications
比较同构和算术应用
  • 批准号:
    261904-2011
  • 财政年份:
    2015
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Comparison isomorphisms and arithmetic applications
比较同构和算术应用
  • 批准号:
    261904-2011
  • 财政年份:
    2014
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Comparison isomorphisms and arithmetic applications
比较同构和算术应用
  • 批准号:
    261904-2011
  • 财政年份:
    2013
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Canada Research Chair in Number Theory
加拿大数论研究主席
  • 批准号:
    1000204643-2007
  • 财政年份:
    2012
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Canada Research Chairs

相似国自然基金

基于Modular积图和最大团的草图形状匹配技术研究
  • 批准号:
    61305091
  • 批准年份:
    2013
  • 资助金额:
    25.0 万元
  • 项目类别:
    青年科学基金项目

相似海外基金

Special values of L-functions and p-adic modular forms
L 函数和 p 进模形式的特殊值
  • 批准号:
    534722-2019
  • 财政年份:
    2021
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Alexander Graham Bell Canada Graduate Scholarships - Doctoral
Deformation in p-adic families of Bianchi modular forms
Bianchi 模形式的 p-adic 族中的变形
  • 批准号:
    2593437
  • 财政年份:
    2021
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Studentship
Adic Modular Forms
Adic 模块化形式
  • 批准号:
    RGPIN-2016-06731
  • 财政年份:
    2021
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Adic Modular Forms
Adic 模块化形式
  • 批准号:
    RGPIN-2016-06731
  • 财政年份:
    2020
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Special values of L-functions and p-adic modular forms
L 函数和 p 进模形式的特殊值
  • 批准号:
    534722-2019
  • 财政年份:
    2020
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Alexander Graham Bell Canada Graduate Scholarships - Doctoral
Special values of L-functions and p-adic modular forms
L 函数和 p 进模形式的特殊值
  • 批准号:
    534722-2019
  • 财政年份:
    2019
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Alexander Graham Bell Canada Graduate Scholarships - Doctoral
Shimura varieties - intersection theory, rigid geometry, stratifications and p-adic modular forms
Shimura 品种 - 相交理论、刚性几何、分层和 p-adic 模形式
  • 批准号:
    RGPIN-2014-05614
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
Study of congruences and p-adic properties for modular forms with several variables
多变量模形式的同余性和 p-adic 性质的研究
  • 批准号:
    18K03229
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Grant-in-Aid for Scientific Research (C)
Adic Modular Forms
Adic 模块化形式
  • 批准号:
    RGPIN-2016-06731
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Discovery Grants Program - Individual
CAREER: Slopes of p-adic Modular Forms
职业:p-adic 模形式的斜率
  • 批准号:
    1752703
  • 财政年份:
    2018
  • 资助金额:
    $ 3.35万
  • 项目类别:
    Continuing Grant
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