Let R be a regular local ring, G be a reductive R-group scheme. A conjecture of Grothendieck and Serre predicts that a principal G-bundle on spec(R) is trivial if it has a rational section.This has been proved in many particular cases. Recently Fedorov and Panin, using previous results of Panin, Stavrova and Vavilov, gave a proof in the case, when R contains an infinite field.

I will discuss the statement of the conjecture, some corollaries, and the strategy of the proof.