Right, and apparently all signatories to the Convention have an obligation to prosecute people who commit "grave breaches" of the conventions, no matter their n

Right, and apparently all signatories to the Convention have an obligation to prosecute people who commit "grave breaches" of the conventions, no matter their nationality and the place the crime took place. So, if a commander from X commits the crime, and the X refuses to prosecute him, he can be legally captured and tried as soon as he visits another signatory country. This is better than just the ICC, definitely (if I understand it correctly).