Serre Duality for Non-commutative P-bundles
نویسنده
چکیده
Abstract. Let X be a smooth scheme of finite type over a field K, let E be a locally free OX -bimodule of rank n, and let A be the non-commutative symmetric algebra generated by E. We construct an internal Hom functor, HomGrA(−,−), 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 HomGrA(OX ,−). When X is a smooth projective variety, we prove a version of Serre Duality for ProjA using the right derived functors of lim n→∞ HomGrA(A/A≥n ,−).
منابع مشابه
Serre Finiteness and Serre Vanishing for Non-commutative P-bundles
Suppose X is a smooth projective scheme of finite type over a field K, E is a locally free OX -bimodule of rank 2, A is the non-commutative symmetric algebra generated by E and ProjA is the corresponding non-commutative P -bundle. We use the properties of the internal Hom functor HomGrA(−,−) to prove versions of Serre finiteness and Serre vanishing for ProjA. As a corollary to Serre finiteness,...
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