Mathematical Sciences: Syzygies and Algebraic Groups

该项目涉及到几个问题， 交换性阿格拉主要调查人员将致力于 霍罗克斯猜想他们还将研究合朔定理 并将某些结果推广到混合特征情形。 另一个集中关注的领域是与 代表群体的积极特征。之一 在这方面要考虑的主要问题是描述如何 张量函子，作用于不可分解的表示， 腐烂 本项目的研究涉及两个方面， 交换代数第一个领域是关于 有限射影合的结构和性质 维度，并使用局部交换代数。“朔望”是 在射影分解中将步骤连接或接合在一起 描述模块的结构。第二个领域是 张量函子在形式群下的分解 定律和相对格罗滕迪克群的性质， 与尸体腐烂有关

This project is concerned with several problems in commutative algera. The principal investigators will work on the Horrocks'conjecture. They will also work on the syzygy theorem and extending certain results to the mixed characteristic case. Another area of concentration concerns invariants related to representations of groups in positive characteristic. One of the main problems to be considered in this area is to describe how tensor functors, acting on indecomposable representations, decompose. The research in this project involves two areas of commutative algebra. The first area is concerned with the structure and properties of syzygies of finite projective dimension and uses local commutative algebra. A "syzygy" is a linking or yoking together of steps in a projective resolution describing the structure of a module. The second area is concerned with decomposing tensor functors under formal group laws and the properties of the relative Grothendieck groups that are associated to the decomposition.