From the article posted earlier:
The 1951 agreement gave the US the authority to "construct, install, maintain, and operate" military installations in specific locations, most notably Thule Air Base (now Pituffik Space Base). Between these locations and across Greenland's national territory, including its territorial seas and airspace, US forces are granted "unrestricted freedom of operation" under Article V. The Kingdom of Denmark's authority over Greenland is expressly acknowledged in the agreement. The US has "exclusive jurisdiction" over its military troops and defensive zones, which includes exemption from several Danish laws and fees.
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Don't know that much about the base. Good up-to-date article that describes all the in's and out's, including the history and current staffing, etc. Sounds to me like the agreement with Denmark basically gives the U,S. carte blanche anyway. So, this seems more about ownership of minerals to me.