Sikkink Johnson, Matthew2024-01-052024-01-052023-10https://hdl.handle.net/11299/259656University of Minnesota Ph.D. dissertation. October 2023. Major: Mathematics. Advisor: Gennady Lyubeznik. 1 computer file (PDF); ii, 37 pages.R. Hartshorne has defined algebraic de Rham homology groups of algebraic varieties over a field k of characteristic 0. N. Bridgland proved that for every affine variety Y over k there is a Hodge-de Rham spectral sequence that starts at E2, is finite-dimensional over k, and converges to the algebraic de Rham homology of Y . Since R. Hartshorne proved that algebraic de Rham homology groups are functorial with respect to some morphisms, including open embeddings, there arises a natural question whether the Hodge-de Rham spectral sequence also is functorial with respect to the same classes of morphisms. While this question in general is very much open, it is proven in this thesis that the answer is positive for open embeddings that are localizations at a single element.enCommutative Algebrade Rham homologyThesis or Dissertation