Does the servant die in this chapter? And what comes after?

The chapter says he "was cut off out of the land of the living" (53:8), that "They made his grave with the wicked, and with a rich man in his death" (53:9), and that "he poured out his soul to death" (53:12). It also says, "he will see his offspring. He will prolong his days" (53:10), "After the suffering of his soul, he will see the light and be satisfied" (53:11), and "Therefore I will give him a portion with the great" (53:12). The chapter doesn't say how both are so, and these notes don't say it for the chapter. Paul writes "that Christ died for our sins according to the Scriptures" (1 Corinthians 15:3), "that he was buried, that he was raised on the third day according to the Scriptures" (1 Corinthians 15:4), and doesn't say there which Scriptures he means.