Serre Finiteness and Serre Vanishing for Non-commutative P-bundles
نویسنده
چکیده
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, we prove that ProjA is Ext-finite. This fact is used in [2] to prove that if X is a smooth curve over SpecK, ProjA has a Riemann-Roch theorem and an adjunction formula.
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