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Writ of Certiorari:

An order issued by the U.S. Supreme Court directing the lower court to transmit records for a case which it will hear on appeal. 

Commonly abbreviated "cert."  If the phrase "cert. denied" appears in the text of a Supreme Court case, it means that the court has denied the appellant's request to hear the case, and thus they deny the petitioner's request to issue the writ of certiorari.