Date of Award
Spring 1-1-2013
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematics
First Advisor
Markus Pflaum
Second Advisor
Sebastian Casalaina-Martin
Third Advisor
Jeanne Duflot
Fourth Advisor
Carla Farsi
Fifth Advisor
Thomas Ivey
Abstract
Recent discoveries make it possible to compute the K-theory of certain rings from their cyclic homology and certain versions of their cdh-cohomology. We extend the work of G. Cortinas et al. who calculated the K-theory of, in addition to many other varieties, cones over smooth varieties, or equivalently the K-theory of homogeneous polynomial rings. We focus on specific examples of polynomial rings, which happen to be filtered deformations of homogeneous polynomial rings. Along the way, as a secondary result, we will develop a method for computing the periodic cyclic homology of a singular variety as well as the negative cyclic homology when the cyclic homology of that variety is known. Finally, we will apply these methods to extend the results of Michler who computed the cyclic homology of hypersurfaces with isolated singularities.
Recommended Citation
Wayne, David, "The K-theory of filtered deformations of graded polynomial algebras" (2013). Mathematics Graduate Theses & Dissertations. 36.
https://scholar.colorado.edu/math_gradetds/36