# nLab algebraic vector bundle

### Context

#### Bundles

bundles

fiber bundles in physics

# Contents

## 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).

## References

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

Last revised on May 25, 2017 at 11:11:09. See the history of this page for a list of all contributions to it.