Hi there,
I know there are fairly straightforward ways to write down the schemes of infinite dimensional projective spaces (not restricting myself to only countable dimensions), but what happens with infinite dimensional *general linear groups* ? Is there a well-known, standard way to define its group scheme, just as in the finite dimensional case ? Or is this usually done using Ind-scheme constructions ? (And if so, can somebody describe it in a nutshell for, e.g., uncountable dimensions ?)


Thanks !!



Group scheme of infinite dimensional linear groups ?
You can write an infinite dimensional general linear group as a filtered colimit of finite dimensional general linear groups, where the filtering is over finite subsets of an infinite basis, ordered by inclusion. This process produces an ind-scheme, since each inclusion is a closed embedding. The basis can be uncountable.


