Politico have a good info piece up if you are interested:

Its worth checking out in full, there are some interesting precedents and nuances. But, if you prefer, in summary:

  • Buy Greenland:

    • Trump could attempt to purchase Greenland if it declares independence from Denmark, making it a U.S. territory or commonwealth.
    • Past U.S. offers to buy Greenland (e.g., 1946) set a precedent, but international laws now discourage buying or selling territories.
    • Greenland's prime minister opposes the idea, emphasizing the island is "not for sale."
  • Economic and Legal Challenges:

    • Greenland holds significant unexplored mineral and hydrocarbon resources.
    • Denmark likely lacks legal authority to sell Greenland, and international recognition of such a deal would be contentious.
  • Military Takeover:

    • A military invasion, while unlikely, has been rhetorically floated but would provoke severe global backlash.
  • Defense and Strategic Agreements:

    • The U.S. could negotiate a Compact of Free Association (COFA) with Greenland, similar to agreements with Pacific islands, granting exclusive military access and economic support.
    • Such a deal could counter China’s Arctic ambitions and bolster NATO’s regional presence.
  • Increased U.S. Military Presence:

    • Trump could expand U.S. military bases and surveillance systems in Greenland, enhancing Arctic and Atlantic security.
    • The U.S. already operates early warning radars at Pituffik Space Base and could increase capabilities to counter Russia and China.
  • Diplomatic Implications:

    • U.S. efforts to influence Greenland could strain relations with Denmark and other allies.
    • Denmark may support greater U.S. involvement due to its limited capacity to defend Greenland.

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Earlier:

US President Trump tweet with a picture of Trump Tower in Greenland

From the first time around ...