nLab algebraic vector bundle

Idea

The notion of vector bundle in algebraic geometry.

Usually characterized in terms of its sheaf of sections on the locally ringed site (with structure sheaf $\mathcal{O}$) of the given scheme: a locally free $\mathcal{O}$-module of finite rank.

Properties

Relation to analytic vector bundles

Over the complex numbers, GAGA relates algebraic to holomorphic vector bundles (e.g. Neeman 07, theorem 1.1.4).

Related concepts

• topological vector bundle

• differentiable vector bundle

• shtuka

References

• Amnon Neeman, Algebraic and analytic geometry, London Math. Soc. Lec. Note Series 345, 2007 (publisher)