Mathematical Sciences: Syzygies and Algebraic Groups

这个项目涉及到交换算法中的几个问题。主要调查人员将对霍罗克的猜想进行研究。他们还将研究合并性定理，并将某些结果推广到混合特征情况。另一个集中的领域涉及与正特征群的表示有关的不变量。在这一领域要考虑的主要问题之一是描述作用于不可分解表示的张量函子是如何分解的。这个项目的研究涉及交换代数的两个领域。第一个领域涉及有限射影维合的结构和性质，并使用局部交换代数。“syzygy”是描述模块结构的投影分解中的步骤的链接或连接在一起。第二个领域涉及在形式群律下分解张量函子，以及与分解有关的相对Grothendieck群的性质。

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.