Monday, the Supreme Court will begin what promises to be an action-packed fall. I’m looking forward to three cases in the first half of October. Here they are, in the order they’ll be argued.

Kiobel vs. Royal Dutch Petroleum Company, Monday: The term opens with a case held over from last year – in a way that doesn’t bode well for Esther Kiobel. She sued Royal Dutch Shell in 2002 on behalf of her late husband and 11 other Nigerians, saying the company colluded with the Nigerian military in the 1990s to silence protesters – going so far as torturing and killing them – who were trying to halt oil exploration. When the court first heard the case, the question was whether corporations could be sued for human rights abuses. Cue lots of bitterness on the left about how the court could treat companies as people for the purposes of campaign donations, but not when it comes to accusations of murder.

Now the case is back to resolve a more basic question: Can Kiobel sue in the United States over this alleged breach of international law on foreign soil? The law at issue is the Alien Tort Statute, passed in 1789 to combat piracy, among other things. No one much used it until the 1980s, when it became a weapon for fighting human rights abuses. In 2004, the court said it was OK to use the statute for claims based in “universally condemned human rights violations.” Genocide, torture and human trafficking should count along with piracy. Will a majority of justices now retreat from that position? Or will conservative justices prefer to read the law based on its historical roots, thus keeping this 1789 statute alive?

Ryan vs. Gonzales and Tibbals vs. Carter, Oct. 9: We are not supposed to execute mentally insane people. The Supreme Court said so in 1986. That’s still the law, though it’s worth worrying over the low standard of competence courts use. Apart from that, what exactly is supposed to happen if a defendant is sentenced to death and then found to be incompetent, because of mental illness, to help his lawyer press his appeals?

Two federal appeals courts have essentially found that defendants have a right to be competent during habeas corpus – basically, a defendant’s last-ditch chance to get off death row. The 9th Circuit stayed proceedings indefinitely in the case of Ernest Valencia Gonzales, who is psychotic, and who killed a man in the course of a burglary. In Ohio, a district court similarly ordered an indefinite stay for Sean Carter, sentenced to die for killing his adoptive grandmother, and then found to be delusional with schizophrenia.

The Obama administration has weighed in against a rule that favors indefinite stays for death row inmates whose mental illness makes them incompetent. It’s too much to ask to stop all these cases, the government says. The American Psychiatric Association is on the other side, arguing that, for the sake of fairness, people who can’t help their lawyers shouldn’t be marched through their appeals. The American Bar Association wants a flexible standard, depending on the level of the defendant’s impairment and the circumstances of the case.

Fisher vs. University of Texas at Austin, Oct. 10: The Supreme Court famously battled its way to a détente over affirmative action in 2003. Two different majorities struck down the use of quotas that favored historically disadvantaged racial minorities in public college admissions but allowed schools to use race as one unquantified factor among many. Justice Samuel Alito is a dedicated foe of race-conscious policies, and that can only be good for Abigail Fisher, who is white, and who was denied admission to the University of Texas at Austin in 2008. UT, abiding by a 1997 state law, fills most of its class – more than 85 percent, the year Fisher applied – with the top 10 percent of the state’s high school graduates. For the remaining spots, the university takes race into account. Fisher wasn’t among the top 10 percent in her high school, so her argument is that she should have gotten one of the remaining spots – and did not because of affirmative action.

The last rationale that the Supreme Court accepted for maintaining some degree of affirmative action was diversity. We’ll see whether their continuing support for affirmative action matters. Justice Elena Kagan will sit this case out – she presumably worked on it during her time in the Obama Justice Department. If the court splits 4-4, Abigail Fisher will lose. But for that to happen, Justice Anthony Kennedy would have to join the liberal-moderate side. He didn’t go that way in 2003, or in the two major cases about race-conscious government policies since. Maybe his vote isn’t a foregone conclusion, though? We’ll know more soon enough.