Which emperor wrote a Greek history of the Etruscans?

The emperor who wrote a Greek history of the Etruscans was Claudius. His work, known as "Historia Etruscorum," is significant as it reflects his interest in Etruscan culture and history, an interest that was somewhat uncommon among Roman elites. Claudius, who was a more scholarly emperor compared to some of his predecessors and successors, engaged deeply with Etruscan studies, demonstrating a curiosity about the origins and contributions of the Etruscans to Roman culture. This perspective also aligned with his broader efforts to establish a scholarly legacy, as he sought to enhance Rome’s understanding of its past and the civilizations that once occupied Italy.

The other emperors listed did not contribute a similar work on the Etruscans. Nero is better known for his artistic pursuits and disasters during his reign, Augustus focused on consolidating his power and promoting a Roman identity, while Tiberius was more focused on governance and military matters than on scholarly writing about ancient cultures. Thus, Claudius stands out as the correct choice for having authored a significant historical narrative on the Etruscans.