When King Rudolph III of Burgundy died on February 2, 1032, Conrad claimed the kingship on the basis of an inheritance that Henry II had extorted from Rudolph in 1006, after Henry invaded Burgundy to enforce his claim in 1016. Despite some opposition, the Burgundian and Provençal nobles paid homage to Conrad in Zürich in 1034. This Kingdom of Burgundy, later known as the Kingdom of Arles under Conrad's successors, corresponded to most of the southeastern quarter of modern France and included western Switzerland, the Franche-Comté, and Dauphiné. It did not include the smaller Duchy of Burgundy to the north, ruled by a cadet branch of the Capetian King of France. (Most of the former Kingdom of Arles was incorporated into France piecemeal over the next centuries, but the King of Arles remained one of the Holy Roman Emperor's subsidiary titles until the dissolution of the Empire in 1806.)