algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

, an ind-scheme is a set-valued functor that can be written (represented) as a

direct limit In mathematics, a direct limit is a way to construct a (typically large) object from many (typically smaller) objects that are put together in a specific way. These objects may be groups, rings, vector spaces or in general objects from any categor ...

(i.e., inductive limit) of closed embedding of schemes.

Examples

\mathbbP^ = \varinjlim \mathbbP^N

is an ind-scheme. *Perhaps the most famous example of an ind-scheme is an

infinite grassmannian In mathematics, the affine Grassmannian of an algebraic group ''G'' over a field ''k'' is an ind-scheme—a colimit of finite-dimensional schemes—which can be thought of as a flag variety for the loop group ''G''(''k''((''t''))) and which descr ...

(which is a quotient of the loop group of an algebraic group ''G''.)

References

*A. Beilinson, Vladimir Drinfel'd, Quantization of Hitchin’s integrable system and Hecke eigensheaves on Hitchin system, preliminary versio

*V.Drinfeld, Infinite-dimensional vector bundles in algebraic geometry, notes of the talk at the `Unity of Mathematics' conference
Expanded version
*http://ncatlab.org/nlab/show/ind-scheme Algebraic geometry {{algebraic-geometry-stub

Examples

See also

References