Let be a field. An ind-variety over is a set along with a filtration:
Each is a finite dimensional algebraic variety over
The ring of regular functions on an ind-variety is defined to be where the limit is taken with respect to the family of maps .
This ring is given the structure of a topological ring by letting each have the discrete topology and have the induced inverse limit topology, i.e. the topology induced from the canonical inclusion and the product topology on .
An ind-variety is called affine (resp. projective) if each is affine (resp. projective).
Let be the ring of formal Laurant series over and be its ring of integers, the formal Taylor series. Let . Then the set of -lattices (-submodules of maximal rank) in is an example of a (non-finite dimensional) projective ind-variety using the filtration
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- 3 Igor Shafarevich, On some infinite-dimensional groups. II Math USSR Izvestija 18 (1982), pp. 185 - 194.
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|Date of creation||2013-03-22 15:30:56|
|Last modified on||2013-03-22 15:30:56|
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