The Supreme Court is trying to sort out whether states can prosecute immigrants who use fake Social Security numbers to get a job.

The justices heard arguments Wednesday in Kansas’ appeal of a state court ruling that threw out three convictions after concluding the state was seeking to punish immigrants who used fake IDs to obtain jobs.

The Kansas Supreme Court ruled that the federal government has exclusive authority to determine whether an immigrant is authorized to work in the United States.

The justices seemed concerned that states shouldn’t be hampered in other identity-theft prosecutions when someone might use a stolen Social Security number to get a driver’s license or arrange for direct deposit of a paycheck.

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