What is the expiation for swearing falsely, and what is the expiation for an oath in general?

The 'Yamin Ghamus' (perjured oath) is an oath sworn upon a lie. It is named as such because it plunges the one who swears it into the Hellfire or into sin, and it is considered a major sin. The majority of scholars hold that it has no expiation (kaffarah) and that its perpetrator is only required to repent. However, the Shafi'is are of the opinion that it can be expiated. The more cautious approach is to combine repentance with expiation.