By Russia editor Steve Rosenberg
The first thing Putin wants from this summit is something he's already been given.
And that's recognition.
Recognition from the world's most powerful country, America, that Western efforts to isolate the Kremlin leader have failed.
The fact that this high-level meeting is happening is testament to that, as is the joint press conference that the Kremlin has announced. The Kremlin can argue that Russia is back at the top table of global politics.
"So much for being isolated," crowed the tabloid Moskovsky Komsomolets earlier this week.
Not only has Putin secured a US-Russia summit, but a prime location for it. Alaska has much to offer the Kremlin.
First, security. At its closest point, mainland Alaska is just 90km (55 miles) from Russia's Chukotka. Vladimir Putin can get there without flying over "hostile" nations.
Second, it's a long way - a very long way - from Ukraine and Europe. That sits well with the Kremlin's determination to sideline Kyiv and EU leaders, and deal directly with America.
There's historical symbolism, too. The fact that Tsarist Russia sold Alaska to America in the 19th Century is being used by Moscow to justify its attempt to change borders by force in the 21st Century.
"Alaska is a clear example that state borders can change, and that large territories can switch ownership," wrote Moskovsky Komsomolets.
But Putin wants more than just international recognition and symbols.
He wants victory. He's been insisting that Russia keep all the land it has seized and occupied in four Ukrainian regions (Donetsk, Luhansk, Zaporizhzhia and Kherson) and that Kyiv withdraw from the parts of those regions still under Ukrainian control.
For Ukraine this is unacceptable. "Ukrainians will not give their land to the occupier," says the country's president, Volodymyr Zelensky.
The Kremlin knows that. But if it secures Trump's support for its territorial demands, the calculation may be that rejection by Ukraine would result in Trump cutting all support for Kyiv. Meanwhile, Russia and the US would get on with boosting relations and developing economic cooperation.
But there is another scenario.
Russia's economy is under pressure. The budget deficit is rising, income from oil and gas exports falling.
If economic problems are pushing Putin to end the war, the Kremlin may compromise.
For now, there's no sign of that - with Russian officials continuing to insist that Russia holds the initiative on the battlefield.
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