Ah, another endgame study! With boths sides having a pawn majority on opposite flanks, this one could make it into a book or DVD on rook and pawn endings. Both sides are looking to create a passed pawn.
My opponent could not resist 35...Rc3. Looks great, and even greater if I obliged him with the exchange of rooks. But, why would I do that? I went 36. Kf3 Re3 37. Ke3 and my king position had gotten better. On e3, my king is still within striking distance of black's B pawn in case it became passed via a4. The problem with this maneuver by black is that it also creates a passed A pawn for white that black cannot ignore. Black continued with 37...Ke6 38. Kd4 ( " Body check " as Karsten Mueller would declare! ) Kd6 39. Kc4, an important move. So, black must decide where to commit his king. He went 39...Kc6 40. g5! The pawns are on auto-pilot to create a passed pawn. So, 40...Kb6? a wasted move. It was necessary to move his king closer to the action via Kd6 or Kd7. The correct move here for white is 41. g6, advancing a pawn one more square and fixing the black pawn on g7. Play went 41...Kc6 42. f5 Kd6 ( can you see how wasteful 40...Kb6 was? ) 43. f6 gf6 44. g7 and game over. 1-0.
White's better king position and advanced pawns on the kingside made this win possible.