Ind-scheme

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

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* C P ∞ = lim -> ⁡ C P N {\displaystyle \mathbb {C} P^{\infty }=\varinjlim \mathbb {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

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* formal scheme

## References

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* A. Beilinson, Vladimir Drinfel'd, Quantization of Hitchin’s integrable system and Hecke eigensheaves on Hitchin system, preliminary version [1] Archived 2015-01-05 at the Wayback Machine
* 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

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