Ethnic population living in the mountainous region of western Asia (most of middle east) spanning southeastern Turkey, northwestern Iran, northern Iraq, and northern Syria are called Kurds.
The region where Kurds mainly live altogether is also called Kurdistan.
The controversy around Kurds/Kurdistan?
Ottoman empire controlled Most western Asia which included so-called Kurdistan.
In the first world war, Ottoman empire got defeated. After its defeat, western allies decided to make provision for a separate Kurdish state for Kurds by the Treaty of Serves, but it never happened.
The Treaty of Lausanne followed the Treaty of Serves. It defined the borders of the modern Turkish Republic but had no provision for a Kurdish state. This left Kurds with minority status in their respective countries(Syria, Turkey, Iraq, etc).
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Fact that a separate Kurdish state (country) could not be established led to numerous genocides and rebellion.
Non-establishment of the Kurdish state is also causing Current ongoing armed guerrilla conflicts in Turkey, Iran, and Syria.
Many armed revolutionary groups are pursuing greater cultural rights, autonomy, and independence by the establishment of Greater Kurdistan.