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arXiv · 2204.02714

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

Christopher Deninger
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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.

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Christopher Deninger. 2022-04-06. There is no "Weil-"cohomology theory with real coefficients for arithmetic curves. https://arxiv.org/abs/2204.02714

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