Intersection Multiplicity, Canonical Element & Related Problems in Algebra

该奖项支持对交换代数中两组主要问题的研究。主要研究者将研究Serre关于完全分支正则局部环的模和Chow群相交多重性的猜想。他还将研究霍赫斯特的正则元猜想及相关问题。本研究涉及交换代数和代数几何中的若干问题。代数几何研究多项式方程族的解。人们既可以研究解集的几何，也可以通过研究解集上的某些函数来代数地解决问题，这些函数形成了所谓的交换环。这种对偶视角在交换代数和代数几何之间建立了紧密的联系。

This award supports work on two sets of major problems in commutative algebra. The principal investigator will work on Serre's conjecture on interesection multiplicity of modules and Chow groups of a complete ramified regular local ring. He will also work on the canonical element conjecture of Hochster and related problems. This research is concerned with a number of questions in commutative algebra and algebraic geometry. Algebraic geometry studies solutions of families of polynomial equations. One can either study the geometry of the solution set or approach problems algebraically by investigating certain functions on the solution set that form what is called a commutative ring. This dual perspective creates a close connection between commutative algebra and algebraic geometry.