Grothendieck Duality on Diagrams of Schemes

Thesis (Ph.D.)--University of Washington, 2015-12The Du Bois complex and Du Bois singularities, which extend results of Hodge theory to singular complex varieties, can be defined in terms of a cubical hyperresolution. In this dissertation I further develop the language of diagrams of schemes and then prove analogues of Grothendieck duality and other cohomological theorems for cubical diagrams. I then demonstrate the use of these by revisiting some known results about the Du Bois complex from a different perspective, and proving new results concerning the cohomology of a contraction