[{"key":"dc.contributor.author","value":"Lawrence, Justin Daniel","language":null},{"key":"dc.date.accessioned","value":"2026-04-03T00:11:21Z","language":null},{"key":"dc.date.available","value":"2026-04-03T00:11:22Z","language":null},{"key":"dc.date.issued","value":"2026","language":"en"},{"key":"dc.identifier.uri","value":"http:\/\/hdl.handle.net\/2429\/93923","language":null},{"key":"dc.description.abstract","value":"The goal of this dissertation is to explicitly construct a rigid dualizing complex for the algebra k[x\u2081, . . . , x\u2099], with k a field, using the methods of [CO24]. Along the way, we give an overviewof the theory of derived categories with the needed results (\u00a71), an overview of the background and methods of [CO24] (\u00a72), and develop some associated tools using cubical homology (\u00a73). In particular, analogous to how [CO24] constructs a rigid dualizing complex for a Hecke algebra by using an exact sequence arising from geometric properties of the associated Weyl group, we do so in this case using an exact sequence arising from a space of translations associated to k[x\u2081, . . . , x\u2099]. This serves as a proof of concept that these methods are generalizable, with hopeful applications to pro-p Iwahori Hecke algebras.","language":"en"},{"key":"dc.language.iso","value":"eng","language":"en"},{"key":"dc.publisher","value":"University of British Columbia","language":"en"},{"key":"dc.rights","value":"Attribution-NonCommercial 4.0 International","language":"*"},{"key":"dc.rights.uri","value":"http:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/","language":"*"},{"key":"dc.title","value":"Rigid dualizing complexes of polynomial algebras","language":"en"},{"key":"dc.type","value":"Text","language":"en"},{"key":"dc.degree.name","value":"Master of Science - MSc","language":"en"},{"key":"dc.degree.discipline","value":"Mathematics","language":"en"},{"key":"dc.degree.grantor","value":"University of British Columbia","language":"en"},{"key":"dc.contributor.supervisor","value":"Ollivier, Rachel","language":null},{"key":"dc.contributor.supervisor","value":"Cautis, Sabin","language":null},{"key":"dc.date.graduation","value":"2026-05","language":"en"},{"key":"dc.type.text","value":"Thesis\/Dissertation","language":"en"},{"key":"dc.description.affiliation","value":"Science, Faculty of","language":"en"},{"key":"dc.description.affiliation","value":"Mathematics, Department of","language":"en"},{"key":"dc.degree.campus","value":"UBCV","language":"en"},{"key":"dc.description.scholarlevel","value":"Graduate","language":"en"}]