For the whole series of articles on the Kurds in Turkey, see here
Since the 19th century, there have been Kurdish people living in the Caucasus. Many had been living in parts of the Ottoman Caucasus when it was annexed by the Russian Empire, but others migrated there, particularly at the time of the Kurdish deportations in 1916. In 1926, there were over fifty four thousand Kurds living in the Soviet Union, the vast majority of them in the Caucasus.
After the Russian Revolution, Soviet policy towards the non-Russian nationalities was confused and disjointed, trying to balance the right to self-determination with the survival of the new workers’ state. The Bolsheviks had inherited the Tsarist Empire, dubbed “the prison-house of nations” by Lenin, and they sought to build a state not governed by Great Russian chauvinism. Local languages were promoted over Russian, and Russian communists who had been placed in positions of authority were replaced by native officials.
This policy of "indigenisation" (korenizatsiia) began in earnest in 1923, and the Kurdistansky Uyezd (uyezd roughly corresponding to an English county) was established as part of the Azerbaijan Soviet Socialist Republic. Commonly known as "Red Kurdistan", this territory had no Kurdish self-governance after 1930, and even at best was hampered by Azeri chauvinism in the leadership of the Azerbaijan SSR. Kurds in Soviet Armenia enjoyed more opportunities to develop their national identity, and much more Kurdish scholarship and language education took place there.
The logic of Stalin’s Great Terror in the late 1930s designated certain ethnicities as “unreliable” elements who might have proved to be a threat to the Soviet Union, particularly in the event of a war. This was particularly applied to groups with more of their population over the border, as with the Kurds in Turkey and Iran. In 1937 3,101 Kurds were deported to Kazakhstan, and in 1944 8,694 Kurds were deported to Central Asia, along with many Hemshins (Muslim Armenians) and the entire Meskhetian Turkish population of Georgia. The Soviet government believed that these people might identify more with Turkey than the USSR, and that the Kurds had been "Turkicised" under the Ottoman Empire.
The tragic irony is that many of the Soviet Union’s Kurds and their families had fled to the Caucasus in 1916 to avoid the Ottoman ethnic cleansing, which was driven by a desire to Turkify them and by fear that they might be disloyal and side with the Russian Army. The Kurdish people have lived at the intersection of multiple empires and would-be imperialist states, and have been shamefully mistreated by all of them.