Napue v. Illinois
From Conservapedia
In Napue v. Illinois, 360 U.S. 264, 272 (1959), the U.S. Supreme Court reversed a conviction because "the false testimony used by the State in securing the conviction of petitioner may have had an effect on the outcome of the trial."
This is the leading precedent for arguing that a conviction should be overturned based on false testimony. Increasingly, however, courts have rejected efforts to overturn convictions even when there is overwhelming proof of perjury.