Mathematics – Rings and Algebras
Scientific paper
2002-10-06
Trans. Amer. Math. Soc. 357 (2005), 1349-1416
Mathematics
Rings and Algebras
72 pages
Scientific paper
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.
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