Short answers, pulled from the story.
The Arverni were a Gallic tribe living in the modern Auvergne region of central France during the Iron Age and Roman period. They were one of the most powerful tribes in ancient Gaul, holding a military hegemony that stretched from the Rhine to the Atlantic coast under kings Luernius and Bituitus.
After Vercingetorix surrendered at the Battle of Alesia, Arverni soldiers were pardoned and their senate was restored to power. The tribe lost its suzerainty over neighbouring peoples but retained the status of civitas libera, a free city-state, and remained prosperous through the Roman period.
Vercingetorix was the son of the Arvernian leader Celtillus and was declared king of the Arverni in 52 BC after raising an army and expelling his opponents from Gergovia. He forged an alliance with at least 15 Gallic tribes and led the combined Gallic revolt against Julius Caesar before surrendering at the Battle of Alesia.
The region of Auvergne takes its name directly from the Gallic tribe the Arverni. The name is attested as ecclesiae Arvenicae in 511 AD, and as Alvernhe in documents dating to around 1071-1127.
Emperor Augustus moved the Arverni capital from Gergovia to a new site called Augustonemetum, which is the city now known as Clermont-Ferrand in France.
Arvernian territory was ceded to the Visigoths in 475 AD. The city's bishop, Sidonius Apollinaris, led a resistance before the territory was ultimately surrendered.