English

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

Algebraic Geometry 2023-01-30 v2 K-Theory and Homology

Abstract

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

Keywords

Cite

@article{arxiv.2204.02714,
  title  = {There is no "Weil-"cohomology theory with real coefficients for arithmetic curves},
  author = {Christopher Deninger},
  journal= {arXiv preprint arXiv:2204.02714},
  year   = {2023}
}

Comments

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