Serre finiteness and Serre vanishing for non-commutative P^1-bundles
| dc.creator | Nyman, A. | |
| dc.date | 2002-10-05 | |
| dc.date | 2009-02-27 | |
| dc.date.accessioned | 2026-07-07T12:47:14Z | |
| dc.date.available | 2026-07-07T12:47:14Z | |
| dc.description | 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-commutative symmetric algebra generated by $\mathcal{E}$ and ${\sf Proj}\A$ is the corresponding non-commutative $\mathbb{P}^{1}$-bundle. We use the properties of the internal $\operatorname{Hom}$ functor $\HU(-,-)$ to prove versions of Serre finiteness and Serre vanishing for ${\sf Proj}\A$. As a corollary to Serre finiteness, we prove that ${\sf Proj}\A$ is Ext-finite. This fact is used in \cite{izu} to prove that if $X$ is a smooth curve over $\operatorname{Spec}K$, ${\sf Proj }\A$ has a Riemann-Roch theorem and an adjunction formula. | |
| dc.description | 9 pages, content changed | |
| dc.identifier | https://arxiv.org/abs/math/0210080 | |
| dc.identifier | http://arxiv.org/abs/math/0210080 | |
| dc.identifier | J. Algebra 278 (2004), 32-42 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/221651 | |
| dc.subject | Rings and Algebras | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 14A22; 16S99 | |
| dc.title | Serre finiteness and Serre vanishing for non-commutative P^1-bundles | |
| dc.type | text |