How to disable Gnome ctrl+alt+down and ctrl+alt+up shortcut?

In general this can happen because the OS (window system) has priority and intercepts this shortcut and stops propagation to your desired application. Solution: Removing the shortcuts using dconf-editor:

• Open a terminal
• sudo apt-get install dconf-tools (or dconf-editor)
• Now run dconf-editor
• in dconf-editor go to: /org/gnome/desktop/wm/keybindings/
• Find switch-to-workspace-down, put ['disabled'] instead of default
• same for switch-to-workspace-up
• quit dconf-editor and you are done

I always have this problem when I want to use some Eclipse IDE shortcuts: https://bugs.eclipse.org/bugs/show_bug.cgi?id=321094

Gnome Settings shows only Super key combination for switching workspaces; even gnome-tweak-tool is not helpful.

Anyway, you can still open dconf and edit the two related keys:

from

org.gnome.desktop.wm.keybindings switch-to-workspace-up ['<Super>Page_Up', '<Control><Alt>Up']

to

org.gnome.desktop.wm.keybindings switch-to-workspace-up ['<Super>Page_Up']

The same for the other key combination.

You can run these commands on the terminal:

gsettings set org.gnome.desktop.wm.keybindings switch-to-workspace-up "['<Super>Page_Up']"
gsettings set org.gnome.desktop.wm.keybindings switch-to-workspace-down "['<Super>Page_Down']"
gsettings set org.gnome.desktop.wm.keybindings move-to-workspace-up "['<Super><Shift>Page_Up']"
gsettings set org.gnome.desktop.wm.keybindings move-to-workspace-down "['<Super><Shift>Page_Down']"

Since you have two monitors and don't need workspace, I will suggest to disable the shortcuts for "Move to workspace above/below":

1. Setting > Devices > Keyboard
2. search "workspace"
3. click on "Move to workspace above", press Backspace, press Set, done.

In fact, I disabled all shortcuts related to workspace...