That depends on what you're trying to say, although I suspect that advisorship is your best choice.
Avoid advisorment. The -ment suffix is usually used with a verb, to create a noun that represents the action itself, or the result of the action: move → movement, pave → pavement. Advisor is a noun itself, so adding -ment doesn't really create a useful word.
Advice suggests that Prof. Snape's involvement in your dissertation may have been limited to suggesting a possible topic for it, which you followed. You could say the same thing about your roommate. I assume that's not what you mean.
If you are trying to say that Prof. Snape is acting in his capacity as advisor to provide guidance as you write your dissertation, then advisorship—which uses the -ship suffix to indicate a position, office, or duty—is your best bet.