User:TakuyaMurata/Affine variety

In algebraic geometry, an affine variety is a subset of

In the language of GAGA, a complex affine variety corresponds to a Stein manifold.

Scheme-theoretic approach
An affine variety is completely determined by its coordinate ring. The scheme theory takes this approach to its limit: it allows to construct a geometric object quite analogous to an affine variety and whose coordinate ring is the given arbitrary ring.