International representatives close to the process say that while that may be true, powerful groups like the Haqqanis could continue an insurgency even if Mullah Omar makes peace with Kabul.
Why would the Taliban talk now?
The civil war that the Taliban had all but won in 2001 has gone into remission with the presence of international forces. If the Taliban were to fight for the whole country again, they may not do so well.
The civil war bubbles beneath the surface, and should it resurface, the former northern warlords who have profited from the U.S. presence would make a Taliban fight for supremacy much harder. In short, they may get a better deal at the table than on the battlefield.
Why has it taken so much time to get talks going?
Karzai on several occasions felt bypassed by backdoor U.S. conversations with the Taliban in Qatar. He reportedly blocked progress. The Taliban also walked out on talks when Taliban prisoners at the U.S. base in Guantanamo Bay were not released as they had expected.
Where is Mullah Omar, and why's that important?
He is widely believed to be in Pakistan, unable to move freely without Pakistan's approval. That's what his supporters believe, although Pakistan has denied it. Pakistan wants a say in Afghanistan's future. If Afghanistan drifted toward Pakistan's archenemy India, its sphere of influence would be upset.
What influence will Pakistan have on the talks?
Agha, Mullah Omar's representative, could not have established an office in Qatar and be in a position to talk to Afghans and Americans without Pakistan's permission. That's the understanding of some in the Taliban, at least.
Karzai and U.S. officials have long accused Pakistan's intelligence agency, the ISI, of supporting the Taliban in Afghanistan. The ISI denies that.
What hiccups can we expect?
Karzai says the next talks must be in Afghanistan. That is unlikely to sit well with Pakistan.
But just to get to this point has been very difficult. For the talks to work, all sides will need to be committed.