From around 220 CE until the tenth century, the major center of Jewish learning and authority was Babylonia. The great academies there developed the arguments we now call the Talmud. The leaders of these academies answered Jewish questions from around the world for centuries.
By the middle of the tenth century, however, the authority that the Babylonian Jewish Academics had held over the other Jewish communities had begun to diminish.
Rabbis had established their own legal schools in Spain, North Africa, and Germany. For a while, these new Jewish centers relied on the responsa from the geonim (plural of gaon; the Jewish authority) of Babylonia.
Gradually, however, the differences in lifestyle and the distance from Babylonia to Spain and Germany encouraged the heads of the German and Spanish legal academies to issue their own authoritative decisions. These became binding on their communities and marked the beginning of the end of the period of the Babylonian Geonate. Babylonia's academies lost their authority over the rest of the Jewish world.
The most obvious split between the Babylonian academies and the German academy in Mainz took place at the beginning of the eleventh century. The leading German rabbi was Gershom, known by German Jewry as Rabbenu Gershom (our Rabbi, Gershom). According to tradition, Rabbenu Gershom wrote four special ordinances which differed with Babylonian Halachah (and Spanish Halachah, for that matter).
First, Rabbenu Gershom declared that a man could have only one wife at a time. This ruling was revolutionary. According to the Mishnah and the Talmud, a man could have four wives at the same time (provided he could keep them fed, clothed, and sexually satisfied). This law continued in both Babylonia and Spain, where Muslim law definitively forbade bigamy, Rabbenu Gershom decreed that only one wife was permitted. This law became binding for all Ashkenazic Jews and established a major cultural split between Sephardic and Ashkenazic Jewry.
In addition, Rabbenu Gershom decreed that a women had to agree to a divorce before a man could give her a get. He also made it a major sin to open and read someone else's mail, thus ensuring the privacy and safety of mercantile transactions between Jewish communities.
Finally, Rabbenu Gershom forbade Jews to remind a Jew forced to convert to Christianity of his previous shame.
Modern scholars challenge whether all these ordinances were actually decreed by Rabbenu Gershom. However, they so clearly marked a change in German Jewry's reliance on Babylonia that they remain significant.
Sources: Gates to Jewish Heritage