 V. I. Chernousov (1989) removed this restriction, by proving the Hasse principle for the resistant "E"8 case (see strong approximation in algebraic groups), thus completing the proof of Weil's conjecture.In 2011, Jacob Lurie and Dennis Gaitsgory announced a proof of the conjecture for algebraic groups over function fields over finite fields.used the Weil conjecture to calculate the Tamagawa numbers of all semisimple algebraic groups.