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The dissertation aims to construct a rigid dualizing complex for polynomial algebras over a field.

April 5, 2026Open Access

Rigid dualizing complexes of polynomial algebras

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The dissertation aims to construct a rigid dualizing complex for polynomial algebras over a field.
Construct a rigid dualizing complex using approaches from existing literature.
Provide background on derived categories and methods from prior work.
Utilize cubical homology to develop related tools.
Employ exact sequences linked to geometric properties of the algebra.
Successfully constructs a rigid dualizing complex for k[x₁, ..., xₙ].
Demonstrates the methods' generalizability with potential applications to other algebras.

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This dissertation constructs a rigid dualizing complex in polynomial algebras, indicating broader applications.

Justin Daniel Lawrence (2026) studied this question.

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