Is it permissible for me to falsely swear before the judiciary that I did not divorce my disobedient wife, in order to detain her until she ransoms herself with money, given that I know that a disobedient wife is not entitled to maintenance or a deferred dowry?

The deferred dowry (mu'akhkhar as-sadaq) is not forfeited by a wife's disobedience (nushooz); rather, only her maintenance (nafaqa) is forfeited. Therefore, if a woman is divorced, her deferred dowry must be paid, and her maintenance is not obligatory if her disobedience is proven. If maintenance is legally mandated, it is permissible to find a Sharia-compliant way to avoid paying it.

It is not permissible to lie before a judge. An oath is taken according to the intention of the one administering it, not the one swearing it. Evasion or insinuation are of no benefit. The Prophet (peace be upon him) warned against swearing a false oath to usurp people's rights. Whoever usurps the right of a Muslim by means of his oath, Allah has made Hell obligatory for him and forbidden Paradise to him.