Motivic homotopy theory
动机同伦理论
基本信息
- 批准号:0801220
- 负责人:
- 金额:--
- 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:2008-07-01 至 2011-06-30
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
In this project, the PI intends to use motivic homotopy theory to create new tools for the study of problems in algebraic geometry. The PI plans to transfer classical obstruction theory to the motivic setting, with the specific goal of understanding the obstructions to finding sections to algebraic fiber bundles over an algebraically closed field. The PI plans to study algebraic cobordism, an algebraic versions of the topological theory of complex cobordism, and to further examine its connection with Donaldson-Thomas theory. Additionally, the PI plans a further study of the Deligne-Goncharov motivic fundamental group. Finally, the PI plans a further study of the motivic Postnikov tower, with the goal of gaining a better understanding of this tower for a variety of interesting generalized cohomology theories on algebraic varieties, as well as for the motives of smooth projective varieties.Homotopy theory is a branch of topology, which deals with fundamental properties of curves, surfaces and shapes of higher dimension. Algebraic geometry, on the other hand, tries to understand the properties of solutions of equations, even when one cannot actually solve the equation explicitly. Creating analogies between the seemingly unrelated fields of algebra and topology has often been a fruitful approach to solving difficult problems in both fields. Morel and Voevodsky have transferred an entire branch of topology, called stable homotopy theory, to the algebraic setting, making ideas from stable homotopy theory applicable to problems in algebra and number theory. The PI plans to take a number of specific constructions from homotopy theory, adapt them to this new setting, and use these constructions to solve problems in algebraic geometry.
在这个项目中,PI打算使用motivic同伦理论为代数几何问题的研究创造新的工具。PI计划将经典的障碍理论转移到motivic环境中,具体目标是理解在代数闭域上找到代数纤维束截面的障碍。PI计划 研究代数配边,复配边的拓扑理论的代数版本,并进一步研究其与唐纳森-托马斯理论的联系。 此外,PI计划进一步研究Deligne-Goncharov motivic基本群。最后,PI计划进一步研究动机Postnikov塔,目的是为了更好地理解这座塔,以便更好地理解代数簇上各种有趣的广义上同调理论,以及光滑投射簇的动机。同伦理论是拓扑学的一个分支,它处理曲线,曲面和高维形状的基本性质。另一方面,代数几何试图理解方程解的性质,即使人们实际上不能明确地解出方程。在代数和拓扑这两个看似不相关的领域之间建立类比,往往是解决这两个领域难题的一种卓有成效的方法。 莫雷尔和Voevodsky转移了整个分支的拓扑,所谓的稳定同伦理论,代数设置,使思想从稳定同伦理论适用于问题的代数和数论。PI计划从同伦理论中提取一些特定的结构,使它们适应这种新的设置,并使用这些结构来解决代数几何中的问题。
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)
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Jerzy Weyman其他文献
Syzygies of Determinantal Thickenings and Representations of the General Linear Lie Superalgebra
- DOI:
10.1007/s40306-018-0282-z - 发表时间:
2018-08-04 - 期刊:
- 影响因子:0.300
- 作者:
Claudiu Raicu;Jerzy Weyman - 通讯作者:
Jerzy Weyman
Semi-invariants of canonical algebras
- DOI:
10.1007/s002290050208 - 发表时间:
1999-11-01 - 期刊:
- 影响因子:0.600
- 作者:
Andrzej Skowroński;Jerzy Weyman - 通讯作者:
Jerzy Weyman
An ADE correspondence for grade three perfect ideals
三年级完美理想的 ADE 对应
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:0
- 作者:
Lorenzo Guerrieri;Xianglong Ni;Jerzy Weyman - 通讯作者:
Jerzy Weyman
Bernstein-Gelfand-Gelfand meets geometric complexity theory: resolving the 2 x 2 permanents of a 2 x n matrix
Bernstein-Gelfand-Gelfand 满足几何复杂性理论:解析 2 x n 矩阵的 2 x 2 常量
- DOI:
10.1016/j.jalgebra.2007.04.018 - 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Fulvio Gesmundo;Hang Huang;Hal Schenck;Jerzy Weyman - 通讯作者:
Jerzy Weyman
Category localization semantics for specification refinements
- DOI:
10.1007/s10472-007-9055-4 - 发表时间:
2007-05-30 - 期刊:
- 影响因子:1.000
- 作者:
Jerzy Tomasik;Jerzy Weyman - 通讯作者:
Jerzy Weyman
Jerzy Weyman的其他文献
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{{ truncateString('Jerzy Weyman', 18)}}的其他基金
Applications of Representation Theory in Commutative Algebra
表示论在交换代数中的应用
- 批准号:
1802067 - 财政年份:2018
- 资助金额:
-- - 项目类别:
Continuing Grant
Free Resolutions and Representation Theory
自由决议和表示理论
- 批准号:
1400740 - 财政年份:2014
- 资助金额:
-- - 项目类别:
Continuing Grant
Collaborative Research: AGNES - Algebraic Geometry Northeastern Series
合作研究:AGNES - 代数几何东北系列
- 批准号:
1064409 - 财政年份:2011
- 资助金额:
-- - 项目类别:
Continuing Grant
Geometric aspects of quiver representations
箭袋表示的几何方面
- 批准号:
0600229 - 财政年份:2006
- 资助金额:
-- - 项目类别:
Continuing Grant
Applications of Quiver Representations to Algebra and Geometry
Quiver 表示在代数和几何中的应用
- 批准号:
0300064 - 财政年份:2003
- 资助金额:
-- - 项目类别:
Continuing Grant
Applications of Representations of Quivers
箭袋表示法的应用
- 批准号:
0070658 - 财政年份:2000
- 资助金额:
-- - 项目类别:
Continuing grant
Varieties Related to Algebraic Group Actions
与代数群动作相关的种类
- 批准号:
9700884 - 财政年份:1997
- 资助金额:
-- - 项目类别:
Standard Grant
Mathematical Sciences: Research in Commutative Algebra
数学科学:交换代数研究
- 批准号:
9102432 - 财政年份:1991
- 资助金额:
-- - 项目类别:
Continuing grant
Mathematical Sciences: Research in Commutative Algebra and Invariant Theory
数学科学:交换代数和不变量理论研究
- 批准号:
8903466 - 财政年份:1989
- 资助金额:
-- - 项目类别:
Continuing grant
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经典和动机稳定同伦理论的计算
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2427220 - 财政年份:2024
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Conference: Motivic and non-commutative aspects of enumerative geometry, Homotopy theory, K-theory, and trace methods
会议:计数几何的本构和非交换方面、同伦理论、K 理论和迹方法
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2328867 - 财政年份:2023
- 资助金额:
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RUI:动机、操作和组合同伦理论
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2204365 - 财政年份:2022
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Analyzing algebraic varieties from the point of view of motivic homotopy theory
从动机同伦论的角度分析代数簇
- 批准号:
2101898 - 财政年份:2021
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本征同伦理论及其在枚举几何中的应用
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