History
Weil checked this in enough classical group cases to propose the conjecture. In particular for spin groups it implies the known Smith–Minkowski–Siegel mass formula.
Robert Langlands (1966) introduced harmonic analysis methods to show it for Chevalley groups. J. G. M. Mars gave further results during the 1960s.
K. F. Lai (1980) extended the class of known cases to quasisplit reductive groups. Kottwitz (1988) proved it for all groups satisfying the Hasse principle, which at the time was known for all groups without E8 factors. V. I. Chernousov (1989) removed this restriction, by proving the Hasse principle for the resistant E8 case (see strong approximation in algebraic groups), thus completing the proof of Weil's conjecture.
Read more about this topic: Weil Conjecture On Tamagawa Numbers
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