Jesus in the Talmud
In the first few centuries CE, there were many sects of Judaism (such as Pharisees, Essenes, and Sadducees) each claiming to be the correct faith. Some scholars treat Christianity, during that era, referred to as Early Christianity, as simply one of many sects of Judaism. Some sects wrote polemics advocating their position, and occasionally disparaging rival sects. Some scholars view the depictions of Jesus in the Talmud as a manifestation of those inter-sect rivalries – thus the depictions can be read as polemics by the rabbinic authors of the Talmud which indirectly criticized the rival sect (Christianity), which was growing and becoming more dominant.
Jews
Without a Temple, Greek-speaking Jews no longer looked to Jerusalem in the way they had before. Judaism separated into a linguistically Greek and a Hebrew / Aramaic sphere. The theology and religious texts of each community were distinctively different. Hellenized Judaism never developed yeshivas to study the Oral Law. Rabbinic Judaism (centered in the Land of Israel and Babylon) almost entirely ignores the Hellenized Diaspora in its writings. Hellenized Judaism eventually disappeared as its practitioners assimilated into Greco-Roman culture, leaving a strong Rabbinic eastern Diaspora with large centers of learning in Babylon.