Serre duality for non-commutative P^1-bundles
环与代数
2015-01-12 v2 代数几何
摘要
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.
引用
@article{arxiv.math/0210083,
title = {Serre duality for non-commutative P^1-bundles},
author = {A. Nyman},
journal= {arXiv preprint arXiv:math/0210083},
year = {2015}
}
备注
Erroneous proof of Lemma 2.6 corrected