Dualizing complexes and perverse modules over differential algebras

By Amnon Yekutieli, James J. Zhang. Compositio Mathematica, 2003

51 citations recorded by the source corpus.

A differential algebra of finite type over a field $\mathbb{k}$ is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated $\mathbb{k}$-algebra. The prototypical example is the algebra of differential operators on a smooth affine variety, when $\text{char}\mathbb{k} = 0$. We study homological and geometric properties of differential algebras of finite type. The main results concern the rigid dualizing complex over such an algebra A: its existence, structure and variance properties. We also define and study perverse A-modules, and show how they are related to the Auslander property of the rigid dualizing complex of A.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/166fee4875a77a7d47cf00b97da869b38179eab7

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Citations in the corpus

Homological Transcendence Degree (2004, methodology): “to B for all i. The following lemma was proved a few times in slightly different versions (e.g., [ 33, Theorem 6.2 ]).”
Derived Categories (2016, background): “This is a result from [186] that we present without a proof.”