[Feature request] Show and hide the alternate screen with keyboard shortcuts

In Terminal.app, it is possible to show the alternate screen with Shift + Cmd + ( down arrow ) and to hide the alternate screen with Shift + Cmd + ( up arrow ).

It would be nice to have the same feature in iterm2, it allows to look at the last typed commands (and outputs) when viewing a man page or editing a file.

Here is a related question on AskDifferent.