Loughner is accused of killing six people and wounding 14 others after opening fire at an event hosted by Giffords in front of a Tucson grocery store on Saturday.
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Loughner, 22, has been described as a loner who had increasingly turned to nihilism and nonsensical rants about the meaning of words and the illegitimacy of the U.S. government.
Investigators carried out a search warrant at the suspect's home and seized an envelope from a safe with messages such as "My assassination," and the name "Giffords" next to what appears to be the man's signature.
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The dead include a nine-year-old girl, a federal judge and a member of Gifford's staff. The latter two individuals' murders were the basis for federal charges which can result in a death penalty ruling: two counts of killing an employee of the federal government carrying out official business.
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On the by the federal government on Sunday, which was announced by FBI Director Robert Mueller, the death penalty charges relate to the murder of Gabriel Zimmerman, a member of Giffords' staff, and the murder of the Chief District Judge John Roll.
Criminal Complaint Against Jared Lee Loughner (pdf)
Both charges state that Zimmerman and Roll were engaged in official duties as employees of the U.S. government when they were killed, making the perpetrator eligible for the death penalty under federal law.
The law specifies that the crime against judges must be connected to their official duties, and even though Roll wasn't scheduled to be at the event, prosecutors have found a link to his official duties.
Prosecutors say Roll specifically went to the event to talk to Giffords about the issue of heavy judicial caseload - one he had been working on with her office. By talking to a U.S. Marshal and Giffords' chief of staff, prosecutors say they were able to determine that Roll did talk to members of the congresswoman's staff about the caseload problem at the event, and that a digital surveillance video at the grocery store shows Roll speaking for several minutes with a staffer.
The federal charges are independent of any murder charges - some of which may also carry a possible death penalty - which may be brought against Loughner by the state of Arizona in the days to come.
In addition to the murder charges, Loughner faces attempted murder charges for the critical wounding of Rep. Giffords and more than a dozen other people.
It is believed the attempted murder of a Member of Congress would carry, at the least, a possible life sentence.