No, a prosecutor can not knowingly make misrepresentations to the court.  Indeed, no one can lie to the court, that includes criminal defense attorneys, prosecutors, witnesses, jurors ,etc.  Candor also known as truth is required.  If you feel that there is a clear violation of the duty to be truthful by the prosecutor you must immediately move to exercise your appellate rights. 

Criminal Appeals have specific deadlines and you must contact an appellate attorney that specializes in criminal appeals immediately.  If you miss a deadline, you may loose your right to appeal an issue forever.