Abstract intersection theory for zeta-functions: geometric aspects

Abstract

We give a further elaboration of our previous works on abstract intersection theory for zeta-functions, emphasizing geometric aspects. We review and streamline Weil's proof of the Riemann hypothesis for curves over finite fields and then present it in cohomological terms. Then by using a spectral interpretation of the Riemann zeta-function we construct a model of our abstract intersection theory for the Riemann zeta-function as an analogue of the cohomological version of Weil's classical intersection theory.