In
algebraic geometry, an ind-scheme is a set-valued
functor
In mathematics, specifically category theory, a functor is a mapping between categories. Functors were first considered in algebraic topology, where algebraic objects (such as the fundamental group) are associated to topological spaces, and m ...
that can be written (represented) as a
direct limit (i.e., inductive limit) of
closed embedding of
schemes.
Examples
*
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
In mathematics, a loop group is a group of loops in a topological group ''G'' with multiplication defined pointwise.
Definition
In its most general form a loop group is a group of continuous mappings from a manifold to a topological group .
...
of an
algebraic group
In mathematics, an algebraic group is an algebraic variety endowed with a group structure which is compatible with its structure as an algebraic variety. Thus the study of algebraic groups belongs both to algebraic geometry and group theory.
Ma ...
''G''.)
See also
*
formal scheme
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
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