PESARO, Italy  One summer day in 1964 a fishing trawler from Fano, a small seaside town a few miles south of this provincial capital on the Adriatic, unexpectedly dredged up a life-size bronze statue from the ocean’s depths. Most likely fashioned in ancient Greece and lost at sea after being looted by Romans, the sculpture is now a centerpiece of the Getty Villa, part of the J. Paul Getty Museum in Los Angeles.

If Italian prosecutors have their way, however, its time in America could soon be at an end.

The statue, called “Victorious Youth” in the Getty catalog but better known as the Getty Bronze (after the museum’s founder), depicts an athlete crowned with an olive wreath. It was originally thought by some archaeologists to be the work of Lysippos, the renowned sculptor of the fourth century B.C., though more recent studies date it to the second or third century B.C. It is widely held to be one of the finest original Greek bronzes to have survived from the classical era (most bronzes from that time are Roman copies), which helps explain why it has been at the heart of a complex legal dispute for decades.

The latest round was fought on Friday, in a court here, where Italian prosecutors and lawyers for the Getty presented closing arguments in a case dealing with one key question: Was the museum acting in good faith when it purchased the statue for a little less than $4 million in 1977?

The Italians assert that the bronze was smuggled out of Italy (after being buried in a cabbage patch and later hidden by a priest) without the proper export papers, and that the museum was willfully negligent in carrying out due diligence before buying the work.