Well, I do know that the first schism between east and west was the Acacian Schism. This revolved around Acacius, Patriarch of Constantinople, and it did concern the christological debates (although this was after the time of Nestorius, and certainly nothing to do with Arianism, which was a dead issue by this stage). Acacius drafted a document known as the "Henoticon" (or "image of unity") which sought to find a formula that everyone could agree on. This was issued by the Emperor Zeno. Unfortunately, as is so often the case with such attempts, both sides rejected it for not going far enough in their own direction. The Monophysites said it should have condemned Chalcedon. The westerners (staunch Chalcedonites to a man) said it should have endorsed Chalcedon more. In 484, therefore, a Roman synod formally condemned Acacius, thereby creating the first official rift between Pope and Patriarch. Although Acacius died in 489, the schism lasted for another thirty years.
However, this has nothing to do with Innocent I, who was Pope from 402 to 417. Innocent is remembered for condemning Pelagianism in 415, persecuting the Novatians in Rome (a non-heretical sect found throughout the empire) and for trying to intervene in the affair of John Chrysostom. Chrysostom, Patriarch of Constantinople, had been deposed by the infamous Synod of the Oak under the machinations of Theophilus of Alexandria (who was basically the Dr Evil of the early church). Innocent, like many, opposed this move, and tried to have Chrysostom rehabilitated. He wrote to him in his exile, and together with the western emperor, Honorius, tried to convene a council to bring him back. But the eastern emperor, Arcadius, would have none of it. However, this was not a formal schism between the two wings of the church, so I'm afraid that if this is the sought-for answer, it's not quite correct.