Ind-scheme explained

In algebraic geometry, an ind-scheme is a set-valued functor that can be written (represented) as a direct limit (i.e., inductive limit) of closed embedding of schemes.

Examples

C P ^{infty} = \varinjlim C P ^{N} is an ind-scheme.

• Perhaps the most famous example of an ind-scheme is an infinite grassmannian (which is a quotient of the loop group of an algebraic group G.)

See also

• formal scheme

References

• A. Beilinson, Vladimir Drinfel'd, Quantization of Hitchin’s integrable system and Hecke eigensheaves on Hitchin system, preliminary version http://www.math.uchicago.edu/~mitya/langlands/hitchin/BD-hitchin.pdf
• 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