nLab
algebraic vector bundle

Context

Bundles

Linear algebra

homotopy theory, (∞,1)-category theory, homotopy type theory

flavors: stable, equivariant, rational, p-adic, proper, geometric, cohesive, directed

models: topological, simplicial, localic, …

see also algebraic topology

Introductions

Definitions

Paths and cylinders

Homotopy groups

Basic facts

Theorems

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 𝒪\mathcal{O}) of the given scheme: a locally free 𝒪\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.