Topics in Commutative Algebra and Algebraic Geometry

交换代数和代数几何专题

• 批准号: 9709757
• 负责人: Roger Wiegand
• 金额: $ 3万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1997
• 资助国家: 美国
• 起止时间: 1997-06-01 至 2000-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9709757&HistoricalAwards=false
• 关键词: Topics; Commutative; Algebra; Algebraic; Geometry

WIEGAND, DMS-9709757 ABSTRACT Topics in Commutative Algebra and Algebraic Geometry This project will be undertaken by the research group in commutative algebra and algebraic geometry at the University of Nebraska--Lincoln. Roger Wiegand and Sylvia Wiegand will study local rings of finite Cohen-Macaulay type. R. Wiegand and Tom Marley will consider homological questions in the theory of local rings. S. Wiegand will study prime ideal structure in Noetherian rings and intermediate rings between a local ring and its completion. Brian Harbourne will investigate resolutions of ideals corresponding to finite sets of points (with multiplicities) in projective space. David Jaffe will study binary linear codes and their connections with the geometry of projective space. Judy Walker will work on coding theory, particularly over commutative Artinian rings. Mark Walker will investigate connections between algebraic I-theory and motivic cohomology. These investigations concern central problems in commutative algebra and algebraic geometry, and many of them are continuations of successful collaborations with researchers at other institutions. This project will allow the research group to continue its active involvement in collaborative research and to maintain its position as a leading research group in commutative algebra and algebraic geometry.

交换代数和代数几何的抽象主题这个项目将由内布拉斯加州大学林肯分校的交换代数和代数几何研究小组承担。Roger Wiegand和Sylvia Wiegand将研究有限Cohen-Macaulay型局部环。R.Wiegand和Tom Marley将考虑局部环理论中的同调问题。S.Wiegand将研究Notherian环和局部环与其完备性之间的中间环中的素理想结构。布赖恩·哈伯恩将研究射影空间中对应于有限点集(具有重数)的理想的分解。David Jaffe将研究二进制线性码及其与射影空间几何的联系。朱迪·沃克将致力于编码理论的研究，特别是在交换的Artin环上。马克·沃克将研究代数I-理论和动机上同调之间的联系。这些研究涉及交换代数和代数几何中的中心问题，其中许多是与其他机构的研究人员成功合作的延续。该项目将使研究小组继续积极参与合作研究，并保持其作为交换代数和代数几何领域领先研究小组的地位。