Topics in Commutative Algebra and Algebraic Geometry

该建议为内布拉斯加大学-林肯的交换代数和代数几何研究组提供了支持。R. Wiegand和S. Wiegand将研究有限Cohen-Macaulay型的局部环。R. Wiegand和Marley将考虑同调问题的理论的地方环。S. Wiegand将研究素理想结构在诺特环和建设涉及一个同态图像的complletion的诺特域。哈伯恩将调查resolutionsof理想对应于有限集的点（与多重性）在射影空间，以及相关问题。步行者将致力于编码理论，包括交换局部Artin环上的编码。M.步行者将调查之间的联系algebraicK-理论和motivic上同调。经常，真实的生活问题涉及许多未知参数，可能与方程是不可能解决的。尽管如此，利用交换代数和代数几何的方法，即使不能得到精确解本身，也可以得到关于解集的许多有价值的描述信息。本计画所讨论的研究课题是关于交换代数与代数几何的中心问题。同样重要的是，其中许多是与其他机构研究人员成功合作的延续。根据这一建议提供的资金将使UNL在交换代数和代数几何方面的研究小组能够继续积极参与合作研究，在研究生的专业发展方面取得成功，并保持其在这些领域的领先研究小组地位。

This proposal provides support for the research group in commutative algebra and algebraic geometry at the University of Nebraska---Lincoln. R. Wiegand and S. Wiegand will study local rings of finite Cohen-Macaulaytype. R. Wiegand and Marley will consider homological questions in thetheory of local rings. S. Wiegand will study prime ideal structure inNoetherian rings and constructions involving a homomorphic image of acompletion of a Noetherian domain. Harbourne will investigate resolutionsof ideals corresponding to finite sets of points (with multiplicities)in projective space, and related questions. J. Walker will work oncoding theory, including codes over commutative local Artinianrings. M. Walker will investigate connections between algebraicK-theory and motivic cohomology.Often, real life problems involve many unknown parameters which may be related by equations which are impossible to solve exactly. Nonetheless, using the methods of commutative algebra and algebraic geometry, much valuable descriptive information can be gotten about the sets of solutions, if not the exact solutions themselves. Theinvestigations discussed in this project concern central problems in commutative algebra and algebraic geometry. Just as importantly, many of them are continuations of successful collaborationswith researchers at other institutions. Funds provided under this proposal will allow the UNL research group in commutativealgebra and algebraic geometry to continue its active involvement in collaborative research, its success in the professional development of graduate students and its maintenance as a leading researchgroup in these areas.