I have a folder which I'd like to remove in my remote repository. I'd like to delete it, but keep the folder in my computer

git rm --cached -r somedir

Will stage the deletion of the directory, but doesn't touch anything on disk. This works also for a file, like:

git rm --cached somefile.ext

Afterwards you may want to add somedir/ or somefile.ext to your .gitignore file so that git doesn't try to add it back.