The U.S. Supreme Court’s new term begins Monday with disputes over climate accountability, religious-school funding, gun laws and immigration — cases with consequences for state and local governments as well as people across the country. The first case on the court’s argument calendar asks whether state and local governments can sue fossil-fuel companies for allegedly misleading the public about the harms of their products. The governments argue that companies’ public statements conflicted with what their own scientists understood, and that communities have borne costs from the alleged deception. Many court observers consider the claims an uphill legal fight for environmental advocates. The court is also set to revisit whether religious schools can receive public money while excluding students or families because of sexual orientation or gender identity. St. Mary Catholic Parish in Littleton, Colorado, is seeking state funding through Colorado’s universal preschool program. The parish says requiring it to admit LGBTQ students and children of gay or transgender parents would violate its religious rights; the state argues that funding the school would conflict with its anti-discrimination law. The justices deadlocked 4-4 on a related dispute last term after Justice Amy Coney Barrett recused herself. That tie left in place an Oklahoma ruling against taxpayer funding for an explicitly religious charter school. Barrett is participating in the Colorado case, which could produce a nationwide precedent on public support for religious education. In December, the court is scheduled to hear a challenge to state and local bans on semi-automatic firearms such as the AR-15. Former U.S. Solicitor General Don Verrilli Jr. has pointed to competing considerations: the rifle’s capacity for rapid fire and the large number of Americans who own such weapons. Gun-rights lawyer Erin Murphy says the dispute raises a central question about who decides which arms people may possess. Immigration policy will also be before the justices. They have agreed to hear a case on whether the Department of Homeland Security can deport migrants to countries other than their countries of origin when those countries refuse to take them. The court has twice blocked lower-court orders that stood in the way of the administration’s policy. The administration has sent thousands of people to countries where they may lack personal ties or language fluency; some have been jailed, and allegations of torture have been raised. A separate immigration dispute concerns the administration’s policy of detaining undocumented immigrants without bond hearings, regardless of how long they have lived in the United States. The court’s work increasingly extends beyond its scheduled arguments. Georgetown law professor Stephen Vladeck says emergency applications have grown sharply during the Trump administration while the number of fully argued cases has fallen. He says the court now issues roughly twice as many full-court rulings on emergency applications as decisions in cases heard through its regular process. Emergency decisions are often made quickly, without oral arguments and with limited explanation. Some lower-court judges, both liberal and conservative, say those rulings do not provide enough guidance. The administration has also sought Supreme Court intervention before appeals courts have ruled, a step that was once unusual. Other disputes could reach the court during the term. Texas, Arkansas, Louisiana and Alabama have enacted laws requiring the Ten Commandments to be displayed in public-school classrooms, in conflict with a 1980 Supreme Court precedent. A split among lower courts could prompt the justices to reconsider that ruling. The court may also take up whether states can regulate Kalshi, a prediction-market company valued at $40 billion, whose markets include sports and political outcomes. Election disputes are another potential flashpoint. If conflicts over voting arise during the midterms, they could reach the justices through the emergency docket, where rulings may come with little time for full briefing or argument. Stanford law professor Pam Karlan says the administration faces a tension between avoiding cases it might lose and pressure from President Donald Trump to bring disputes before the Supreme Court. Vladeck cautions that the term’s most consequential cases may not yet be on the docket.