Questions on Local Cohomology and Tight Closure Theory
关于局部上同调和紧闭理论的问题
基本信息
- 批准号:1500613
- 负责人:
- 金额:$ 22万
- 依托单位:
- 依托单位国家:美国
- 项目类别:Standard Grant
- 财政年份:2015
- 资助国家:美国
- 起止时间:2015-06-01 至 2020-05-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
This project is concerned with several questions in commutative algebra. This is a field that studies solution sets of polynomial equations. Understanding solution sets of polynomial equations is of fundamental importance in many sciences, in engineering, and in other disciplines as well. Most of the questions that will be investigated deal with the nature of the solution sets: some are questions that have been unresolved for a number of years, but for which recent advances provide the likelihood of a solution; others arise naturally from new developments in the area. A number of projects are connected with local cohomology theory: this theory often provides the best answers to basic questions such as the least number of polynomials needed to define a solution set.The projects on local cohomology theory include algorithmic aspects, as well as structural properties such as support and injective dimension. There is a special focus on local cohomology modules of polynomial rings and hypersurfaces over the integers: this stems from the fact that there is a canonical homomorphism from the integers to any ring, and this makes local cohomology modules over the integers, in a sense, universal; this viewpoint has proved useful in recent work of the PI and collaborators. The project will also investigate local cohomology over the integers. The research will further develop the connections of local cohomology with prime characteristic numerical invariants such as the F-pure threshold, and will study the composition series of local cohomology modules over rings of differential operators.
这个项目涉及交换代数中的几个问题。 这是一个研究多项式方程解集的领域。 了解多项式方程的解集在许多科学、工程和其他学科中具有根本的重要性。 大多数的问题,将调查处理的性质的解决方案集:一些问题,已经解决了数年,但最近的进展提供了一个解决方案的可能性;其他自然产生的新的发展领域。 许多项目都与局部上同调理论有关:该理论通常为基本问题提供最佳答案,例如定义解集所需的最少多项式数量。局部上同调理论的项目包括算法方面,以及结构性质,如支撑和内射维数。 有一个特别关注的局部上同调模的多项式环和超曲面的整数:这源于这样一个事实,即有一个典型的同态从整数到任何环,这使得局部上同调模的整数,在某种意义上,普遍的;这一观点已被证明是有用的,在最近的工作PI和合作者。该项目还将研究整数上的局部上同调。 该研究将进一步发展局部上同调与素特征数值不变量如F-纯阈值的联系,并将研究微分算子环上局部上同调模的合成序列。
项目成果
期刊论文数量(2)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
Stabilization of the cohomology of thickenings
- DOI:10.1353/ajm.2019.0013
- 发表时间:2016-05
- 期刊:
- 影响因子:1.7
- 作者:B. Bhatt;Manuel Blickle;G. Lyubeznik;Anurag Singh;Wenliang Zhang
- 通讯作者:B. Bhatt;Manuel Blickle;G. Lyubeznik;Anurag Singh;Wenliang Zhang
Homogeneous prime elements in normal two-dimensional graded rings
普通二维渐变环中的齐次素数元素
- DOI:10.1016/j.jalgebra.2018.07.012
- 发表时间:2018
- 期刊:
- 影响因子:0.9
- 作者:Singh, Anurag K.;Takahashi, Ryo;Watanabe, Kei-ichi
- 通讯作者:Watanabe, Kei-ichi
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Anurag Singh其他文献
Higher matching complexes of complete graphs and complete bipartite graphs
完全图和完全二分图的更高匹配复合体
- DOI:
10.1016/j.disc.2021.112761 - 发表时间:
2020 - 期刊:
- 影响因子:0
- 作者:
Anurag Singh - 通讯作者:
Anurag Singh
Discovery of Potent and Selective Covalent Inhibitors of HER2WT and HER2YVMA.
HER2WT 和 HER2YVMA 的强效选择性共价抑制剂的发现。
- DOI:
- 发表时间:
2024 - 期刊:
- 影响因子:7.3
- 作者:
E. Hicken;Karin Brown;Natalie C Dwulet;J. Gaudino;Erik P Hansen;Dylan P Hartley;John P Kowalski;Ellen R Laird;Nicholas C. Lazzara;Bin Li;Tung;Marie F Mutryn;Lauren Oko;Spencer P Pajk;Robert W Pipal;Rachel Z Rosen;Russell A Shelp;Anurag Singh;Jing Wang;C. E. Wise;Christina E Wong;Jim Y Wong - 通讯作者:
Jim Y Wong
The fungal ligand chitin directly binds and signals inflammation dependent on oligomer size and TLR2
真菌配体几丁质直接结合并根据寡聚体大小和 TLR2 发出炎症信号
- DOI:
10.1101/270405 - 发表时间:
2018 - 期刊:
- 影响因子:0
- 作者:
K. Fuchs;Yamel Cardona Gloria;Olaf;Franziska Herster;L. Sharma;C. Dillen;Christoph Täumer;Sabine Dickhöfer;Zsofia Bittner;Truong‐Minh Dang;Anurag Singh;Daniel Haischer;Maria A. Schlöffel;Kirsten J. Koymans;Tharmila Sanmuganantham;Milena Krach;Nadine A Schilling;F. Frauhammer;L. Miller;T. Nürnberger;S. Leibundgut;Andrea A. Gust;B. Maček;M. Frank;C. Gouttefangeas;C. D. Dela Cruz;D. Hartl;A. Weber - 通讯作者:
A. Weber
Ensemble Learning with Hybrid Modelling for Multivariate AQI, PM2.5, and PM10 Forecasting in Mumbai
使用混合建模进行集成学习,用于孟买的多元 AQI、PM2.5 和 PM10 预测
- DOI:
10.1109/cset58993.2023.10346745 - 发表时间:
2023 - 期刊:
- 影响因子:0
- 作者:
Anurag Singh;Pratham Soni;Deepa Krishnan;Ishaan Potle - 通讯作者:
Ishaan Potle
Anurag Singh的其他文献
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{{ truncateString('Anurag Singh', 18)}}的其他基金
Invariant Rings, Frobenius, and Differential Operators
不变环、弗罗贝尼乌斯和微分算子
- 批准号:
2349623 - 财政年份:2024
- 资助金额:
$ 22万 - 项目类别:
Continuing Grant
Local Cohomology, Differential Operators, and Determinantal Rings
局部上同调、微分算子和行列环
- 批准号:
2101671 - 财政年份:2021
- 资助金额:
$ 22万 - 项目类别:
Continuing Grant
Determinantal Rings, Local Cohomology, and Tight Closure
行列式环、局部上同调和紧闭
- 批准号:
1801285 - 财政年份:2018
- 资助金额:
$ 22万 - 项目类别:
Continuing Grant
Local cohomology, tight closure, and related questions
局部上同调、紧闭性及相关问题
- 批准号:
1162585 - 财政年份:2012
- 资助金额:
$ 22万 - 项目类别:
Standard Grant
Tight Closure, Local Cohomology, and Related Questions
紧闭、局部上同调及相关问题
- 批准号:
0600819 - 财政年份:2006
- 资助金额:
$ 22万 - 项目类别:
Standard Grant
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具有粘性逆Lax-Wendroff边界处理和紧凑WENO限制器的自适应网格local discontinuous Galerkin方法
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