MathOverflow is a question and answer site for professional mathematicians. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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 !!

share|cite|improve this question
up vote 3 down vote accepted

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.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.