B737-700 DIVERTS TO A CIVIL ARPT FOLLOWING A CARGO FIRE WARNING ALARM ULTIMATELY DETERMINED TO HAVE BEEN FALSE.

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APPROX 5-10 MINS AFTER LEVELING AT FL400; WE NOTED THE FIRE BELL; RED FIRE WARNING LIGHTS; AND INDICATION OF AN AFT CARGO COMPARTMENT FIRE. WE CANCELED THE BELL AND RAN THE QRH CHKLIST; NOTING THAT THE 'AFT DET 2' CIRCUIT BREAKER WAS POPPED AND THAT THE SYS TESTED BAD ON THE AFT LOOP. WE CONSULTED WITH THE FLT ATTENDANTS AND DEADHEADING CAPT WHO HAD NO ABNORMAL INDICATIONS IN THE CABIN. COMPLETING THE QRH CHKLIST; WE NOTED ZZZ APPROX 80-100 NM AHEAD AND ELECTED TO DIVERT THERE. WE DECLARED AN EMER WITH ATC AND COMMUNICATED WITH DISPATCH DURING THE DSCNT INTO ZZZ. IN THE INTEREST OF EXPEDITING OUR LNDG; WE EXERCISED CAPT'S EMER AUTH TO EXCEED 250 KIAS BELOW 10000 FT. THE ILS APCH AND LNDG AT ZZZ WERE UNEVENTFUL. LNDG WT APPROX 110000 LBS; AUTOBRAKES 2 AND LIGHT MANUAL BRAKING STOPPED THE ACFT NEAR TXWY Z ON RWY 10. WE AWAITED CLRNC FROM THE FIRE VEHICLES BEFORE WE TAXIED CLR AND IN TO GATE. PAX DEPLANED NORMALLY AT THE GATE. WE WROTE UP THE INDICATIONS IN THE LOGBOOK AND CONSULTED WITH DISPATCH AND MAINT CTL OVER THE PHONE AND WITH CONTRACT MAINT FACE-TO-FACE. THE LCL POLICE OFFICERS REPEATEDLY REQUESTED DETAILED PERSONAL INFO FROM THE CAPT. I GAVE A BRIEF VERBAL NARRATIVE OF 'WHY WE DIVERTED' TO THE AIRFIELD OPS CHIEF AND THE POLICE OFFICER EVENTUALLY ACCEPTED WHAT WE PROVIDED HIM WITH THE COMMENT THAT HE WOULD NOTE IN HIS RPT THAT THE CAPT DID NOT PROVIDE ADDRESS/DATE OF BIRTH; ETC. THE PAX WERE ACCOMMODATED ON ANOTHER ACFT; AND THE CAPT AND I DEADHEADED ON THAT ACFT TO OUR ORIGINAL DEST AND ON TO ZZZ1 TO RESUME OUR PAIRING THE FOLLOWING DAY. BASED ON ALL INDICATIONS; THE CARGO FIRE DETECTION SYS EVIDENTLY MALFUNCTIONED. WE NEVER SAW ANYTHING BEYOND THE INITIAL INDICATION THAT WOULD CONFIRM THE PRESENCE OF A FIRE.