Something remarkable happened last week, though it didn’t get the attention it deserved: A long and brutal war came to an end.

For more than four decades, the Kurdish militant group known as the PKK waged an insurgency against the Turkish state that left some 40,000 people dead and reshaped the lives of millions. The PKK’s announcement on May 12 that it had “fulfilled its historical mission” and was ending the armed struggle it has waged since 1984 got little notice outside Turkey, partly because the world was distracted by Donald Trump’s flattery tour of the Persian Gulf monarchies. But that’s the way it often is with wars: magnetic at the start, ignored when the violence fades. “War makes rattling good history,” the novelist Thomas Hardy observed a century ago, “but peace makes poor reading.”

The PKK’s decision to disarm came two months after its imprisoned founder and leader, Abdullah Öcalan, issued a statement suggesting that the war had become obsolete. Öcalan had held secret meetings with the Turkish government for a year, but the content of those talks remains a mystery, and it is still far from clear what the PKK—or the Kurds more broadly—stands to gain from the group’s decision to forswear violence and instead focus on “building a democratic society,” as their announcement put it.

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The Turkish government now has an opportunity to consolidate the peace by offering some kind of amnesty to the PKK’s fighters, who have not yet handed over their abundant weapons, and by addressing the grievances that sparked the war in the first place: more cultural rights and respect for the Kurds, an ethnic group that makes up about 18 percent of Turkey’s population. The Kurds are also substantial minorities in Syria, Iraq, and Iran, where the PKK insurgency had important spillover effects.

If Turkey fails to seize the moment, the conflict could erupt again. That has happened before. I was there the last time peace talks between the state and the PKK broke down, in 2015, and I saw the consequences up close. Cities and towns across southeastern Turkey were bombed, more than 1,000 people were killed in the following months, and thousands of activists and members of pro-Kurdish parties were thrown in prison on trumped-up charges. Many remain there.

So far, President Recep Tayyip Erdoğan has described the PKK’s decision as a victory against terrorism. But the PKK is expecting political concessions from Turkey, including amnesty for its fighters and a broader recognition of Kurdish political and cultural rights. As one of the group’s leading figures, Murat Karayilan, said last week: “We believe the armed struggle must end—but unless the state makes legal changes, peace won’t be possible in practice.”

The PKK’s leaders see their latest move less as a surrender than as the advent of a new phase in their movement, which has long promoted an ideology—leftist, secular, environmentalist—that sits uncomfortably with Erdoğan’s Islamist authoritarianism. That was apparent in the video the group released last week, showing a group of its leaders in combat fatigues, chanting an oath to Öcalan. “I will fight against the dominant and state-worshipping system that dominates our civilization,” they said in unison. “I will keep alive all the values created by the PKK.”

Öcalan has been living in isolation on the prison island of Imrali, in the Sea of Marmara, since his capture in 1999. Now a white-haired 77-year-old, he maintains a cultish authority over the PKK; his portrait hangs everywhere, and he is known by the reverential moniker Apo (“Uncle”). About 20 years ago, he became a devotee of Murray Bookchin, the late Jewish eco-anarchist then living in Vermont, and integrated Bookchin’s thinking into the PKK’s doctrine.

The government has been extremely guarded in its comments about Öcalan and the PKK’s decision, but the viability of the new arrangement will depend on what it offers the group in exchange for relinquishing its weapons. “If they offer too little, that’s a problem for the PKK and its supporters,” Aliza Marcus, the author of Blood and Belief, a history of the movement, told me. If the government appears to be granting too much, that could anger Erdoğan’s right-wing-nationalist coalition partners, who tend to see Kurds as a threat to Turkish unity. That Öcalan will be released is very unlikely, for example, and his top deputies are expected to be given some kind of asylum in other countries. But many rank-and-file PKK members may be allowed to return to their old life.

One possible point of division lies in Syria, where an affiliate of the PKK has run a de facto statelet in that country’s northeast for the past decade, holding up Öcalan as its ideological leader. Erdoğan said the new announcement would apply to the Syrian affiliate, known as the Syrian Democratic Forces. But the leaders of the SDF have made clear that they will not be bound by it.

Within Turkey, whatever the outcome of the political give-and-take between Erdoğan and the PKK, this peace effort seems likelier to hold than its predecessors, in part because the PKK has lost some of its earlier advantages. The Turkish military has developed killer drones and other technologies that allow it to hold Kurdish leaders under siege even in remote strongholds in the Qandil mountains of Iraqi Kurdistan. And many Kurds have grown weary of the war, which has made their life miserable for decades.

The Kurds also have something to offer Erdoğan. He has hinted through proxies that he wants to change Turkey’s constitution so that he can remain in power after his second term as president ends in 2028—but that would be difficult without the support of the Kurdish political parties. The Kurds would also like to see a revised constitution: one that would modify the definition of Turkish nationality—now framed in ethnic terms that make them feel excluded—to a more civic model.

Erdoğan has never actually proposed this cynical quid pro quo, but comments by some of his allies suggest that it is at the core of the presumptive agreement with the PKK. If so, he is taking a risk. Changing the constitution would likely require a popular referendum, and polls suggest that most Turks oppose an amendment to allow the president a third term. Even the Kurds may balk.

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“If the constitution is not democratic, people won’t vote for it,” says Ceylan Akça, a parliamentarian who represents the city of Diyarbakir, in southeastern Turkey, for the pro-Kurdish party known as DEM.

Many ordinary Kurds have high expectations, Akça told me. They hope to see Kurdish political prisoners released from jail, greater tolerance for their language and culture, and a revision to the country’s anti-terrorism law, which is now written in a way that appears to target Kurds. Above all, Akça said, they want a more inclusive understanding of what it means to be a Turkish citizen, whether that is reflected in the constitution or in government policies.

Akça traveled around Turkey in recent weeks, alongside other legislators, holding town-hall-style meetings to help ordinary Kurds make sense of the PKK’s decision to stop fighting. Many of the gatherings were emotionally wrenching, she told me; a lot of the participants had lost family members in the insurgency.

“I saw a lot of people crying as they watched the announcement,” Akça told me. “It’s the end of an era.” Her own message, she said, was to reassure people that a more peaceful and democratic day was coming.

“Now is the right time for the state to tell people they don’t need to be afraid,” she said.