IN 2007 a Russian-led polar expedition, descending through the icy waters of the Arctic Ocean in a Mir submarine, planted a titanium Russian tricolour on the sea bed 4km (2.5 miles) beneath the North Pole. “The Arctic has always been Russian,” declared Artur Chilingarov, one of the polar explorers. In the event, fears that the action would set off a scramble for Arctic territory and riches proved unfounded. Over the next few years the Arctic Council (a talking shop for governments with territories inside the Arctic Circle, and others who attend as observers) became much more influential and one of the few remaining border disputes there (between Norway and Russia) was settled.

Now Denmark has staked a claim to the North Pole, too. On December 15th it said that, under the UN Convention on the Law of the Sea (UNCLOS), some 900,000 square kilometres of the Arctic Ocean north of Greenland belongs to it (Greenland is a self-governing part of Denmark). The timing was happenstance. Claims under UNCLOS have to be made within ten years of ratification—and the convention became law in Denmark on December 16th 2004. But its claim conflicts with those of Russia, which has filed its own case under UNCLOS, and (almost certainly) Canada, which plans to assert sovereignty over part of the polar continental shelf (see map).

The prize for these countries is the mineral wealth of the Arctic, which global warming may make more accessible. Temperatures in the region are rising at twice the rate of the rest of the Earth. According to the United States Geological Survey, the area has an eighth of the world’s untapped oil and perhaps a quarter of its gas.

Hitherto most people have assumed that competition to develop these resources would be gentlemanly. The Arctic, a Norwegian admiral told a big conference two years ago, is “probably the most stable area in the world”. Drilling for oil and gas there is extremely expensive, and falling oil prices have made the economics of Arctic energy even less favourable. This gives would-be prospectors an interest in co-operating, not in adding to the risks and costs.

The melting of the summer sea ice has also opened up trade routes between Asia and Europe via the top of the world; 71 cargo ships plied the north-east passage last summer, up from 46 in 2012. And trade requires rules. Moreover, under UNCLOS, most of the known energy and mineral reserves are within countries’ 200-nautical mile economic zones anyway. So everyone has an interest in minimising conflicts and amicably settling those that crop up.

But reasons for restraint are not always proof against sabre-rattling—and Russia has been indulging in that of late. In addition to annexing Crimea, this summer it carried out extensive combat exercises in the Arctic for the first time since the end of the cold war. It is re-equipping old Soviet bases there and in July tested the first of its new-generation rockets, called the Angara, from a cosmodrome in the high north. Sweden spent part of the summer searching for a Russian submarine that it suspected of slipping into its territorial waters.

Denmark’s claim will test whether Russia is willing to stick to the rules in the Arctic. It is based on a provision of the law of the sea which says countries may control an area of seabed if they can show it is an extension of their continental shelf. (Denmark argues that the Lomonosov ridge, which bisects the Arctic, starts in Greenland.) All Arctic countries, Russia included, have promised to respect this law.

In 2007 the Russians understood the advantages of doing so. “When Russian divers planted their flag on the North Pole seabed,” says Per Stig Moller, a former Danish foreign minister, “I chided my Russian counterpart by saying: ‘Just because you plant a flag there doesn’t mean you own it.’ To which he replied: ‘Just because the Americans plant a flag on the Moon...’”