Definition
Ind-scheme
A functor presented as a filtered colimit of schemes, usually along closed immersions.
Definition
An ind-scheme over a field is a functor on -algebras admitting a presentation
by schemes whose transition maps are closed immersions. It is ind-projective if the can be chosen projective.
The presentation is not part of the object: two filtered systems define the same ind-scheme when their colimit functors are isomorphic.
References
- Alexander Beilinson and Vladimir Drinfeld, Chiral Algebras, American Mathematical Society, 2004, §7.11.