The goal of this dissertation is to explicitly construct a rigid dualizing complex for the algebra k[x₁, . . . , xₙ], with k a field, using the methods of . Along the way, we give an overviewof the theory of derived categories with the needed results (§1), an overview of the background and methods of (§2), and develop some associated tools using cubical homology (§3). In particular, analogous to how 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[x₁, . . . , xₙ]. This serves as a proof of concept that these methods are generalizable, with hopeful applications to pro-p Iwahori Hecke algebras.
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