Kohli, who will lead India in the World Test Championship final against New Zealand from June 18 and the five-match Test series against England, is fifth with 814 points behind England skipper Joe Root.
Pant and Sharma are joint sixth with 747 rating points each. Sharma, who was placed eighth in the previous cycle, has moved one spot past New Zealand batsman Henry Nicholls, who is now in eighth spot.
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Conway, is the latest to enter the ICC Test rankings after his double century against England in the drawn first Test at Lord's that ended earlier this week. He is placed 77th with 447 rating points, the highest for a New Zealand batsman on debut and the third highest ever on debut.
In the Test bowling rankings, India spinner, R. Ashwin continues to hold the No. 2 position (850 rating points), behind Australian pace bowler Pat Cummins, who has 908 points. Ashwin is the only Indian in the top 10.
The top position in the Test all-rounder rankings continues to be held by West Indies' Jason Holder, who is part of the squad for the two-match Test series against South Africa beginning in St.Lucia on June 10.
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Indian all-rounders Ravindra Jadeja (386 points) and Ashwin (353) are second and fourth, respectively. Jadeja has moved up one place, displacing England all-rounder Ben Stokes.