Some noteworthy cases the Supreme Court will hear in its new term that begins Monday:

Church-state separation: A Missouri church is challenging its exclusion from a state program that reimburses groups for installing rubberized surfaces on playgrounds. The Trinity Lutheran Church’s application for a grant was highly rated, but state officials said a provision of the Missouri Constitution bars them from giving public money to a church.

Disparaging trademarks: The Obama administration is defending the decision to deny trademark protection to an Asian-American band called the Slants because the term is offensive to Asians. A lower court struck down the part of federal law on which the decision was based and the outcome of the case also could affect the Washington Redskins football team in its fight to preserve lucrative trademark protection.

Texas death penalty appeals: Two inmates on Texas’ death row are seeking to have their death sentences overturned. Inmate Duane Buck, who is African-American, contends his lawyers failed him by calling as an expert witness a psychologist who testified that black people were more likely to commit violence. Inmate Bobby Moore argues that he is ineligible to be executed because he is intellectually disabled. Moore says Texas courts used outdated standards to reject his claim.

Insider trading: The court will consider a disagreement between lower courts about how to evaluate whether people are illegally benefiting from trading on information from corporate insiders.

Redistricting: Cases from North Carolina and Virginia focus on lawsuits from African-Americans who complain that Republican-led legislatures improperly concentrated Democratic-leaning black voters in some districts to limit their influence in others, ensuring the election of more Republicans.

Citizenship: A man who is facing deportation claims he can’t be removed from the U.S. because he was a citizen at birth. He is challenging an unusual provision of U.S. law that applies to children born outside the country to one parent who is an American and one who is not. The law makes it easier for children whose mother is a citizen to become citizens themselves.

Two appeals that have been filed but not yet acted on also could be heard this term:

Transgender rights: A Virginia school district is appealing a lower court ruling requiring it to allow a transgender boy to use the boys’ bathroom at his high school. The Supreme Court has put the ruling on hold, pending its decision on whether to hear the case.

Voter ID: Texas is asking the high court to overturn a lower court ruling that found that the state’s 2011 law requiring photo identification to vote discriminated against minorities and the poor. Appeals in voter ID cases from North Carolina and Wisconsin also could reach the court, but the justices will not confront the issue until after the November elections.