(from the story of Esther)
Is there historical proof that this ruler lived? He had issued a command to kill all the Jews in his kingdom. It was later rescinded. I'd like to know if this story is just a traditional tale or if any archaeological proof exists that this happened?
The name "Ahasuerus" is Latinized from Hebrew Akhashwerosh and is by all appearances a corruption of Old Persian Khshayarsha (literally, reigns-over-men, cf e.g. the Greek name Anaximandros) via Babylonian Akhshiyarshu; this name is better known through its Greek form Xerxes.
The only Achaemenid king this name could conceivably refer to would be Xerxes I (486 - 465 BC), famous for his invasion of Greece, as his grandson Xerxes II reigned for less than two months. This is also strongly indicated by the mention in Ezra, which notes him as succeeding Koresh (Cyrus) and Daryawsh (Dareios), the latter being the father of Xerxes I.
So did Xerxes reign "from India to Ethiopia over 127 provinces"? Yeah, pretty much. The Achaemenid Empire at its height stretched from the river Sindh in Pakistan to Nubia south of today's Egypt. I am not sure from where they get "127 provinces"; the empire was divided into twenty-odd "Lands", commonly known as satrapies due to the Governor being referred to as the xshaca-pawan or protector of royal power, but it is certainly conceivable that some lower-level administrative divisions could make it all sum to over a hundred provinces. Xerxes' father, Dareios, had built a great palace in Susa, one of the many building works he undertook after implementing his administrative reforms and taking in an absurd amount of tribute, and this must be the citadel referred to in Esther.
So, did Xerxes issue commands to kill all Jews? As far as anyone knows, no, and I don't think many scholars of the Hebrew Bible believes it either. As a side note, though, it is noteworthy that Xerxes declares in one of his royal inscriptions that he destroyed a temple which housed "daiva worshippers", something that may or may not have actually happened. Even if it did, though, it is very unlikely that this referred to any campaings against Jews, as the general line of thought on relations between the Achaemenid line and Judah today is that the Great King enjoyed the support of the priesthood in a claim to kingship traditionally held by the Davidic line, see e.g. Shayegan's recent anthology on Cyrus the Great for more on this.