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arXiv · 2206.14253

Sur la cohomologie \'etale de la courbe de Fargues-Fontaine

Sebastian Bartling
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Abstract

In this article the \'etale cohomology of constructible torsion sheaves on the \'etale site of the algebraic resp. adic Fargues-Fontaine curve is analyzed. In the $\ell\neq p$-torsion case, two conjectures of Fargues are verified: vanishing in degrees greater than two and the comparison between the \'etale cohomology of the adic and the algebraic curve. In the $p$-torsion case, under a certain assumption, the vanishing of the \'etale cohomology in degrees greater than two of those Zariski-constructible sheaves on the adic curve that come via pullback from the algebraic curve is proven.

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Sebastian Bartling. 2022-06-28. Sur la cohomologie \'etale de la courbe de Fargues-Fontaine. https://arxiv.org/abs/2206.14253

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