Mathematical Sciences: Residues, Traces and Relative Fundamental Classes

主要研究者将继续研究有限维固定基格式上有限型平面态射基本类的基本全局理论及其与用微分形式的残数、迹和Hochschild同调表示的局部理论的关系。我们将尝试用一种双变量理论来组织这些结果。阿拉普拉将研究杜波依斯奇点。他将通过考虑如何证明理性奇点是杜波依斯来研究它们。这个项目属于代数几何领域。李普曼将致力于以一种有用的方式阐述格罗滕迪克理论。Arapura将研究代数变量中的奇点，这些变量中的点在几何上是顶点，折痕等等。

The principal investigator will continue studying the basic global theory of the fundamental class of a flat morphism of finite type over a fixed finite dimensional base scheme and its relation to the local theory as expressed via residues and traces of differential forms and Hochschild homology. An attempt will be made to organize the results within a bivariant theory. Arapura will study DuBois singularities. He will study them by considering the problem of showing that rational singularities are DuBois. This project is in the area of algebraic geometry. Lipman will work on formulating the Grothendieck theory in a useful way. Arapura will work on singularities in algebraic varieties, those places in the varieties that are geometrically cusps, creases and so forth.