In 2004, he left Clapp, Peterson and Stowers when he was appointed a Superior Court Judge for the Third Judicial District in Anchorage by Governor Frank Murkowski.
Frank Murkowski (born 1933), U.S. politician, Senator (1981–2002) and Governor of Alaska (2002–2006)
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Incumbent Frank Murkowski (R), first elected governor in 2002, ran for reelection but was defeated in a landslide in the Republican primary by former Wasilla mayor Sarah Palin on August 22, 2006.
On March 31, 2005, Governor Frank Murkowski appointed Márquez as Attorney General for the State of Alaska.