Serre finiteness and Serre vanishing for non-commutative P^1-bundles

A. Nyman

Suppose $X$ is a smooth projective scheme of finite type over a field $K$, $\mathcal{E}$ is a locally free ${\mathcal{O}}_X$-bimodule of rank 2, $\mathcal{A}$ is the non-commutat…