The film has been nominated for Norway's Oscar entry and won the Grand Prix at the Cannes Film Festival earlier this year. Skarsgård plays a former famous film director who tries to reconnect with his daughters and his lost career. Elle Fanning and Renate Reinsve also appear.
American media have previously speculated whether the performance in Trier's film could give Skarsgård his first Oscar nomination.
Swedish composer Ludwig Göransson was also nominated by LAFCA for the music in the horror film "Sinners", but did not win an award.
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