Serre duality for non-commutative P^1-bundles

Abstract

Let E be a locally free, rank n bimodule over a smooth projective scheme X, and let A be the non-commutative symmetric algebra generated by E. We construct an internal Hom functor on the category of graded right A-modules. When E has rank 2, we prove that A is Gorenstein by computing the right derived functors of the internal Hom functor. When X is a smooth projective variety, we use the Gorensteinness of A to prove a version of Serre duality on Proj A, the non-commutative P^1 bundle defined by A.

Erroneous proof of Lemma 2.6 corrected

References in corpus (2)

• Blowing up non-commutative smooth surfaces
• Points on quantum projectivations

Cited by in corpus (3)

• The Grothendieck Group of a Quantum Projective Space Bundle
• Noncommutative Tsen's theorem in dimension one
• Serre finiteness and Serre vanishing for non-commutative P^1-bundles