[2] Korobov won the Ukrainian Chess Championship in 2002, 2012,[3] 2018,[4] 2020 and finished second behind Andrei Volokitin in 2004.

[8] Korobov took clear third place in the Ukrainian Championship of 2013, behind Yuriy Kryvoruchko and Ruslan Ponomariov respectively.

In the World Cup 2013 in Tromsø, Norway he eliminated Vasif Durarbayli, Baadur Jobava, Daniil Dubov and Hikaru Nakamura, but in the fifth round he was knocked out by former World Chess Champion Vladimir Kramnik, after losing the first game and drawing the second.

[14][15] The next month, he played on the silver medal-winning Ukrainian team at the 42nd Chess Olympiad in Baku.

In 2018, he won an individual gold medal at the 43rd Chess Olympiad as the best player on the reserve board.