In 70 AD, the people of the prince rebelled and went against the Romans. The city was destroyed. Well, no one knows exactly who torched the temple. But, either way, the actions of the Jewish people in Jerusalem brought down the fury of the Roman armies. Whether the Jews burned it or the Romans did is rather a moot point.
Desolations are determined to the end of the war.
At the end, when Jerusalem was destroyed is when the desolation ended. And he shall confirm the covenant with many for one week. He says to them that love him and that keep his commandments. It's a covenant that Jesus merely strengthened. It is the covenant that He gave to Abraham.