Depth Properties of Modules Over Local Rings

WIEGAND98-01309该奖项支持同调和交换代数的研究。三个相关的主题将被研究：局部环的同调理论，局部环上的模的表示理论和域上非代数闭的代数簇的Picard群。交换代数通过形成一个称为环的代数对象来研究多项式或幂级数方程的解。通过这些一般解的代数性质，我们可以深入了解方程的几何和代数性质。该领域结合了许多其他领域的技术，包括组合学、拓扑学和分析。

WIEGAND98-01309This award supports research in homological and commutative algebra. Three related topics will be investigated: homological theory of local rings, representation theory of modules over local tings and Picard groups of algebraic varieties over field that are not algebraically closed.Commutative algebra, among other things, studies the solutions of polynomial or power series equations by forming an algebraic object, called a ring, which consists of the 'generic' solutions. The algebraic properties of these generic solutions then give insight into the geometric and algebraic nature of the equations. The field combines techniques from a number of other areas including combinatorics, topology, and analysis.