When Weil proposed his famous conjectures, he noted that the rationality and functional equation parts would follow from the existence of a cohomology theory with suitable properties. In my talk, I will discuss the axioms of such a cohomology theory and how it applies to the Weil conjectures. If time permits, I will touch upon how the analogue of the Riemann hypothesis follows from the standard conjectures on algebraic cycles. Speaker(s): Patrick Lenning (UM)