As reported to the FAA. Reports are unverified, and codes are left as the FAA publishes them.
What was found
AFTER TAKEOFF, CLIMBING TO 1750 FEET AGL, BAGGAGE COMPARTMENT SMOKE DETECTOR WARNING LIGHT ILLUMINATED. NO INDICATION OF SMOKE WAS PRESENT, ACFT TURNED AROUND & LANDED WITHOUT FURTHER INCIDENT. TROUBLE SHOT SYS & REPLACED SMOKE DETECTOR. OPERATIONS CHECKED SYS, NO FURTHER PROBLEMS NOTED.