Year: 2002
Type: preprint
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.
Source: arXiv (Cornell University)
Author: Nyman, A.
Institution: University of Montana
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2949102162