Mystery is my favorite genre and I love historical mystery most of all. Some of my favorite historical mysteries are set in Roman times. I love Kelli Stanley'sRoman Noir books Nox Dormenda and The Curs-emaker, andthe books by Steven Saylor. But the first historical Roman mystery I ever read was Lindsey Davis' Silver Pigs, published in 1989. It was not her first novel, but the first in her "Falco" series of historic mysteries. Read her biography here.
If you'd like to explore historical mysteries set in Rome, check out the website The Detective and the Toga. the first listing in the events section mentions Lindsey Davis' new book Enemies at Home. Wikipedia also has a really good article on the mystery subgenre. Read it here.