Abstract
The first two sections of this note are an expanded version of the lecture at the Congress. We first explain how a cohomological formalism might look, one that would serve the same purposes for zeta functions of number fields and étale or cristalline cohomology for zeta functions of curves over finite fields. After indicating some consequences of the hypothetical formalism that can actually be proved, we explain how very naturally the Riemann hypotheses would ensue. These matters are also discussed in [De2] but in the much more general framework of motives. We thought that it might be useful to make the simple basic ideas available to non experts for motives as well.
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Deninger, C. (1994). Evidence for a Cohomological Approach to Analytic Number Theory. In: Joseph, A., Mignot, F., Murat, F., Prum, B., Rentschler, R. (eds) First European Congress of Mathematics . Progress in Mathematics, vol 3. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9110-3_16
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