There is no "Weil-"cohomology theory with real coefficients for arithmetic curves

Abstract

A well known argument by Serre shows that there is no Weil cohomology theory with real coefficients for smooth projective varieties over ${\bar{\mathbb{F}}}_p$. In this note we explain why no "Weil-"cohomology theory with real coefficients can exist for arithmetic schemes over spec $\mathbb{Z}$, even for spectra of number rings.

arXiv commentFinal version for publication in Annali della Scuola Normale Superiore di Pisa, Classe di Scienze