The consequence of the joint rejection of God by the priests and the people of Judaea was called the "desolation" by Daniel and by Jesus-Holy Ghost in paragraph 095.

What, exactly, was the "desolation" to be?
Jesus provided several descriptions of the "desolation". One description is in paragraph 093, wherein the destruction of the entire Temple complex was prophesied. Another description is in paragraph 095, wherein the "desolation" was also called the "great tribulation". An additional description is in paragraph 103, wherein the temporary disappearance of the nation was prophesied.

When was the desolation formally announced?
Jesus-Holy Ghost formally announced the desolation to the priests and people in paragraph 109. This announcement was apparently before their formal announcement to him of their rejection. The priests formally announced their rejection of him in paragraph 126 and, along with the people, again in paragraph 128.

Did the desolation occur?
The desolation occurred during and after two rebellions of Judaea against the Romans. The first of these two rebellions began in 66 AD and ended in 73 AD. In the midst of this rebellion, beginning in 70 AD,  the Romans destroyed the entire Temple complex and the city of Jerusalem. The second of these two rebellions began in 132 AD and ended in 135 AD. After the second of these two rebellions, the Romans deported nearly everybody from Judaea to a multitude of different places in the Roman empire (mainly to the frontiers of the Roman empire), thereby fulfilling the prophesy (in paragraph 103) that the nation would temporarily disappear.

Did the nation ever re-appear?
The nation officially re-appeared in 1948. It was named Israel when it re-appeared. More details of the history since the desolation to the present are available here.