Although Cumbria was previously believed to have formed the core of the Early Middle Ages Brittonic kingdom of Rheged, more recent discoveries near Galloway appear to contradict this. For the rest of the first millennium, Cumbria was contested by several entities who warred over the area, including the Brythonic Celtic Kingdom of Strathclyde and the Anglian kingdom of Northumbria. Most of modern-day Cumbria was a principality in the Kingdom of Scotland at the time of the Norman conquest of England in 1066 and thus was excluded from the Domesday Book survey of 1086. In 1092 the region was invaded by William II and incorporated into England. Nevertheless, the region was dominated by the many Anglo-Scottish Wars of the latter Middle Ages and early modern period and the associated Border Reivers who exploited the dynamic political situation of the region. There were at least three sieges of Carlisle fought between England and Scotland, and two further sieges during the Jacobite risings.