This happened following his brilliant innings of 254* in the second Test against South Africa.
Smith continues to top the batsmen rankings with 937 rating points, with Kohli being on 936.
Records scripted by Kohli in 2nd Test
Following are the records scripted by Kohli in the second Test:
He has the most number of double centuries in Tests by an Indian (7).
He surpassed Don Bradman in terms of most 150-plus scores in Tests (9).
He has most Test runs as Indian captain, going past Sunil Gavaskar.
He has scored the second-most Test centuries as captain, along with Ricky Ponting (19).
Other Indian batsmen
Mayank Agarwal continues his rise, Ravindra Jadeja too in limelight
As Kohli looks to topple Smith in the third Test in Ranchi, opener Mayank Agarwal continued his steady rise in the rankings with a fine knock of 108 in the second Test.
As a result, he has risen to the 17th spot (657 points).
Meanwhile, Ravindra Jadeja too made a jump, to the 40th spot, with 551 rating points.
Ravichandran Ashwin and Umesh Yadav shine among bowlers
Talking about the Indian bowling contingent, off-spinner Ravichandran Ashwin continued to grab headlines as his six-wicket haul in Pune allowed him to rise to the seventh spot.
Further, pacer Umesh Yadav, who too claimed six wickets, has risen to 25th (600 rating points).
Meanwhile, Jadeja and Ashwin maintain their second and fifth spots in the all-rounder category.
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Three South Africans show activity in the rankings
As far as the rankings of South Africans are concerned, three players have shown some activity. Among batsmen, Vernon Philander and Keshav Maharaj have displayed escalation, rising to 82nd and 115th each. Among the bowlers, it is spinner Senuran Muthusamy, who has risen to 114th.
India on top
India consolidate top spot in Test rankings and World Championship
Notably, India continue to dominate the top spot in team rankings, with 115 rating points, while South Africa are on the third spot, with 108 points.
As for the ICC World Test Championship, India continued to consolidate the top spot with 200 points, having won four matches so far, while South Africa are yet to collect a single point.