Mathematical Sciences: Residues, Traces and Relative Fundamental Classes

主要研究人员将继续研究固定有限维基格式上有限类型平坦态射基本类的基本整体理论，以及它与通过微分形式的余迹和Hochschild同调所表示的局部理论的关系。将尝试在双变量理论中组织结果。阿拉普拉将研究杜波伊斯奇点。他将通过考虑证明有理奇点是Dubois的问题来研究它们。这个项目是在代数几何领域。利普曼将致力于以一种有用的方式阐述格罗森迪克理论。阿拉普拉将研究代数簇中的奇点，即代数簇中几何尖点、折痕等的位置。

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.