Forensic tests have shown a man who jumped to his death from a Glasgow hotel was being sought by police over the murder of Sally Geeson.
Miss Geeson's body was found in woodland at a cemetery
Officers investigating the death of the Cambridge student had wanted to question Lance Corporal David Atkinson.
He set himself alight and jumped from the Corus Hotel on Saturday.
The naked body of Miss Geeson, 22, was found on Friday in a cemetery near Cambridge, three miles from where she was last seen after a new year party.
It is understood L/Cpl Atkinson, 31, who served with the 23 Engineers, came from Glasgow.
He was based at the Royal Engineers' Waterbeach barracks near Cambridge.
Sally Geeson's disappearance
1 Jan: Sally Geeson last seen leaving a New Year's Eve party in Cambridge
3 Jan: Cambs Police make appeal for information
7 Jan: A body is found at Madingley, near Cambridge
8 Jan: The body is identified as Miss Geeson
9 Jan: Police say that a man found dead in Scotland was a suspect in the case
10 Jan: Police carry out forensic tests on the man
Det Supt Willie Johnston, of Strathclyde Police, said officers from Cambridgeshire had travelled to Strathclyde as part of their investigation.
The Ministry of Defence revealed on Monday that L/Cpl Atkinson had been cleared in 1998 of kidnap and assault charges relating to a Polish woman, while serving in Germany.
The Royal Military Police knew L/Cpl Atkinson was in Cambridge on the night of 31 December and that he had been due to report for duty on 4th January.
He failed to do so, and Cambridgeshire Police were alerted by the Royal Military Police.
L/Cpl Atkinson's body was found outside the hotel, on one of the main streets in central Glasgow, a few hundred yards from the city's main railway station.
Ms Geeson's body was found by a man walking in a wooded area of the World War II American Military Cemetery in Madingley.
The murder inquiry team confirmed scientists were attempting to establish if she had been sexually assaulted before her death.
A forensic science student, Ms Geeson, from Southend, Essex, was due to start her final exams at Anglia Polytechnic University this week.