Is a divorce considered to have occurred if a man, jokingly, says "yes" to his wife in response to her question, "What, are you looking for the marriage certificate because you're going to divorce me?"

If a man says to his wife: "Yes, I will divorce you," this does not constitute a divorce, because it is a promise of divorce in the future. There is no difference in divorce between seriousness and jest, due to the Prophet's (peace be upon him) saying: "There are three things whose seriousness is serious and whose jest is serious: marriage, divorce, and revocation."