(see also *Chern-Weil theory*, parameterized homotopy theory)

**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**

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.

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

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

Last revised on May 25, 2017 at 15:11:09. See the history of this page for a list of all contributions to it.