Sky knows Iraq well, having served as adviser to the commanding general of US forces in Iraq from 2007 to 2010 and as the governorate coordinator of Kirkuk for the Coalition Provisional Authority , the US-led transitional government that temporarily administered Iraq after the 2003 invasion, from 2003 to 2004.

To get a better understanding of what's going on in Kirkuk and what it means for the future stability of Iraq, I reached out to Emma Sky, director of the Greenberg World Fellows Program at Yale University and the author of The Unraveling: High Hopes and Missed Opportunities in Iraq .

Now, many fear the fight over Kirkuk and Kurdish independence could end up destabilizing the country all over again.

The Kurdistan Regional Government in Erbil — despite strong opposition from the United States and much of the international community — hastily called an independence referendum on September 25, brazenly including Kirkuk in the vote as a way to establish their control over the contested city. The Iraqi government responded by sending troops into Kirkuk, driving Kurdish forces out. Twenty-two Kurdish fighters were killed in the skirmish.

But now that Iraqi and Kurdish forces have pushed ISIS out of most of the country, those old divisions between Baghdad and Erbil have reared up again.

When ISIS erupted on the scene in the spring of 2014, this fight over Kirkuk — and over Kurdish independence more generally — got largely shunted to the back burner as both Baghdad and Erbil focused on kicking ISIS out of the country.

The Kurds want Kirkuk to be part of a future independent state of Kurdistan, controlled from its capital, Erbil. The Iraqi central government, on the other hand, wants to keep Kirkuk — along with the rest of Iraqi Kurdistan — as part of a unified Iraq, controlled by Baghdad.

The Iraqi central government in Baghdad and the semi-autonomous region of Iraqi Kurdistan are fighting over control of Kirkuk , a multiethnic region in northeastern Iraq that sits atop some of the country's most lucrative oil fields. It's an area that has been a flashpoint between the country's Arab majority and the Kurdish minority on and off for decades.

America's two main allies in the fight against ISIS in Iraq are now in a shooting war with each other over control of an oil-rich city — a fight that has the potential to throw Iraq into chaos and possibly even full-scale civil war.

Sean Illing

Let's start with the most recent news in Iraq, which is the fighting between the Kurds and the Iraqi government over Kirkuk. Why is this significant?

Emma Sky

It's significant because since 2003, the Kurds have been looking to take control of Kirkuk, to annex it to Kurdistan, because they see Kirkuk and all its [oil] wealth as essential to them gaining an independent Kurdistan.

It all came to a crisis after the referendum was held on September 25. The referendum was held in disputed territories, including Kirkuk, and that was a step too far for the central government [in Baghdad].

Iraqi Prime Minister Haider al-Abadi has national elections coming up next year, and no Iraqi prime minister can afford to lose Kirkuk. He urged the Kurds not to move forward with the referendum. They did it anyway, and he responded by sending Iraqi troops into Kirkuk.

Sean Illing

Is Iraq on the brink of a renewed civil war?

Emma Sky

Well, it's important to remember that Iraq has basically been in civil war since 2003. From the US perspective, we've been focused on the fight against ISIS, but the Iraqis and the Kurds have been looking ahead to the day after the ISIS fight for a long time.

During the fight against ISIS, the Kurds received weapons directly from the international community and extended their control over what are called the "disputed territories," including Kirkuk. Now that ISIS is virtually defeated, the Iraqi government, supported by Shia militias, is trying to push back on Kurdish expansionism.

Sean Illing

For someone who doesn't follow Iraq as closely as you, it's hard to make sense of Kurdish President Masoud Barzani's decision to hold this independence referendum. Why do it now?

Emma Sky

It's baffling in some ways, but this is a very complex situation, and the Kurds themselves are divided over it. Barzani, the president of the Kurdistan Regional Government, believed this was the right time to move toward independence because he thought the Kurds were at their strongest position. They've got weapons. They're holding key territories. So he felt the referendum would increase his position in negotiations with Baghdad.

He also wanted to rally Kurds around the flag. His term as president actually expired two years ago, and he's facing a lot of domestic criticism. People are accusing him of mismanagement, of stealing oil, and of corruption. So there wasn't full support among different Kurdish parties to push ahead with this referendum. They saw it as a move by Barzani to try and strengthen his position.

Sean Illing

How big a blunder was it by Barzani to hold this referendum?

Emma Sky

Here's the thing: It was only an opinion poll. It wasn't a formal declaration of independence. But I think Barzani made a gamble, and I think he expected that there would be opposition from the neighboring countries, particularly Iran. I'm not sure he expected such opposition from the US, and I don't think at all that he anticipated the amount of internal divisions this would provoke within Kurdistan.

To answer your question, I think it was a colossal miscalculation.

Sean Illing

What becomes of America's relationship with the Kurds now that they've gone down this road?

Emma Sky

It's a very sad situation because we have been close to the Kurds for a long time. It was our intervention after the first Gulf War that led to the Kurds gaining this autonomous area. They were part of the coalition to bring down Saddam in 2003. The relationships are personal, and they're very strong.

But we also have a relationship with the government of Iraq. So now we're in a situation where our allies are squaring off against each other. There's no real solution to that.

Sean Illing

Kirkuk is also a diverse and integrated city. There's no way to divide it up without causing massive problems, right?

Emma Sky

Yeah, it's very diverse and ethnically mixed. You've got Arabs, Kurds, Turks, Christians, Sunnis, Shia — it's a very mixed population and they've been intermarrying for a long time, and they have an identity as Kirkukis. If you start asking people if they want to be a part of Iraq or Kurdistan, you're going to pull people apart.

But if more thought went into Kirkuk having some sort of special status, so it could be a region in its own right with special relations with Erbil and with Baghdad, that might work. It would have to be an empowered region in its own right, so that locals could choose their leadership and be empowered to manage their own affairs. That's a feasible solution that is a win for everyone involved.

Sean Illing

If that doesn't happen, if the fight escalates, whose side will America be on?

Emma Sky

Well, that was the question that President Barzani asked me to pass on to the Americans when I was working in Iraq in 2010: When Arabs and Kurds start fighting each other, whose side are you on? It's a situation that America's got every interest to prevent from happening. It is not in Prime Minister Abadi's interest or Barzani's interest to get into a civil war. They kind of need each other to get out of the situation that they're in.

Sean Illing

Right, but if they do start fighting each other, what do you think America will do?

Emma Sky

Probably what we've done before: come in and try to mediate. A political deal has been struck before, so it's possible that this can be resolved without war. But the last thing we want to do is put more weapons in the hands of each side and sit back while they use them against one another. We have a very strong interest in mediating this conflict and helping to negotiate a border that both sides can live with.

Sean Illing

Your best guess: What does Iraq look like in 5 or 10 years?

Emma Sky

My best guess is that it will keep bumbling on like this. I don't think we'll get to a full-scale war between Arabs and Kurds. I think they will reach an agreement where there is a confederation for Iraqi Kurdistan. I expect some of the border will still be disputed. I expect there will be a joint administration in Kirkuk.

I think Iran will still be the major external actor but the Iraqi state will be stronger, institutions will be stronger, and the economy will be doing better. I realize that may sound overly positive, but Iraqis have sort of hit bottom already, and now I think they can start to work back up.

Sean Illing

You're the expert, but that sounds wildly optimistic to me.

Emma Sky

No one could've predicted a week ago that Kirkuk was going to be taken over on Monday, and yet it happened with almost no bloodshed. So sometimes things happen in unexpected ways. There's a national election in Iraq scheduled for next year. Will that lead to the Iranian-supported Shia militias taking power, or will Prime Minister Abadi manage to come through all this having gained credit for defeating ISIS and resolving the Kurdish crisis?

Look, schools are opening again in Mosul. Mosul has just been through a horrific experience in their battle with ISIS. And they're out there opening schools and building universities. The resilience of the Iraqis is quite extraordinary, and despite everything, when you ask young Iraqis, they see a vision of the future. They see their future much better than the last few years. They haven't given up.

And that gives me hope.