None of us really know what Putin and Trump have discussed behind closed doors in their various meetings. Word is leaking out that in one of those meetings Putin made a claim on Alaska. He pulled out old family photos and discussed how his family was run out of Alaska by the American bankers and land speculators. Putin used Trump penchant for feeling like the victim to explain how the American bankers bullied and stole his family land. Apparently hundreds of thousands of acres according to Putin.
It seems Putin has told Tump that Alaska is nothing but a frozen wasteland most of the year and is useless to the US, but it has a sentimental value to Putin and Russia.
As for the US military bases in Alaska, Putin said he would compensate Trump/USA appropriately at a later date. Needless to say the Pentagon sees things in an entirely different light.