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Siegel's theorem on integral points for higher dimensional varieties

What is know about a generalisation of Siegel's theorem on integral points for higher dimensional varieties?

I found https://books.google.de/books?id=0jt8CwAAQBAJ&pg=PA21&lpg=PA21&dq=siegelt+theorem+for+higher+dimensional+varieties&source=bl&ots=fERGN2quJV&sig=OCfjVZxPyxmG6sU1mQpNxspufrY&hl=de&sa=X&ved=0ahUKEwjw5sXWxPjRAhXBuRQKHcJDBvcQ6AEIJjAA#v=onepage&q=siegelt%20theorem%20for%20higher%20dimensional%20varieties&f=false

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