WASHINGTON — The Supreme Court begins hearing cases this week, but none of them looks to be a high-profile legal dispute that will split the eight justices.

Here are a few notable legal questions due to be decided in the new term:

Insider trading: Is it a crime for people to buy stock based on tips that came from family members or friends who in turn learned it from a corporate insider? The lower courts are divided on the reach of the federal laws that forbid insider trading. Bassam Salman, a grocery wholesaler from Chicago, was indicted and convicted for trading on tips that came from a brother-in-law in California, who in turn learned the corporate secrets from another brother who worked at an investment bank. (Salman vs. United States, to be heard on Wednesday)

Race and death penalty: Is it unconstitutional to sentence a black defendant to death after the jury had been told blacks are more likely to pose a danger to society? Duane Buck, who murdered two people in Houston in 1995, has been trying to challenge his sentence as racially biased, but state and federal judges have repeatedly refused to give him a hearing because it was his lawyer, not the prosecutor, who first introduced the biased testimony. (Buck vs. Davis, Wednesday)

Aid to church schools: Is it unconstitutional to exclude a church school from taking advantage of a state program that provides recycled crushed tires for playgrounds? At least 35 state constitutions prohibit using tax money for churches and their schools. Religious-rights advocates say these common provisions discriminate against religion and thereby violate the U.S. Constitution. (Trinity Lutheran Church vs. Pauley, not yet scheduled for argument.)

Immigrants held for deportation: Do immigrants who face deportation either because they committed a crime or were picked up at the border have a right to a bail hearing and possible release if they are held in jail for six months? Acting on a suit brought by ACLU lawyers in Los Angeles, the 9th Circuit Court ruled these detainees are entitled to a bail hearing after six months and to be released unless the government can show they present a danger or a flight risk. Obama administration lawyers object to what they call a "radical revision" of the deportation laws. (Jennings vs. Rodriquez, not yet scheduled.)

Police and false arrests: Can someone who was wrongly arrested and held in jail for seven weeks because a police officer fabricated evidence of illegal drugs then sue the city for "malicious prosecution"? The Supreme Court has hinted at but never ruled directly that people who are victims of such police misconduct may sue for a violation of their constitutional rights. The 7th Circuit Court in Chicago tossed out such a claim filed by a Joliet man, but the justices will hear his appeal. (Manuel vs. Joliet, Wednesday.)

Trademarks and free speech: May the government refuse to issue a trademark for an Asian American rock band that calls itself the Slants because the term is judged to be offensive and disparaging? A federal appeals court ruled the refusal violated the free speech rights of the band's founder, who chose the name precisely because it had been a slur. Washington's pro football team, the Redskins, is fighting in court over the same issue. (Lee vs. Tam, will be heard early next year.)