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.

Included in

Mathematics Commons

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