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.
