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arXiv · 2010.09182

Faisceaux Q/Z(j) et conjecture de Gersten sur un corps imparfait

Alexandre Lourdeaux
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Abstract

On revoit explicitement la construction ainsi que certaines propri\'et\'es des complexes de faisceaux \'etales $\mathbb{Q}/\mathbb{Z}(j)$ sur certains sch\'emas. Le but de ces notes est d'avoir une r\'ef\'erence pr\'ecise pour la conjecture de Gersten pour les faisceaux $\mathbb{Q}/\mathbb{Z}(j)$ sur un corps imparfait ainsi que pour la comparaison entre les groupes de cohomologie $\mathrm{H}^2(\ast,\mathbb{Q}/\mathbb{Z}(1))$ et $\mathrm{H}^2(\ast,\mathbb{G}_m)$. We review explicitly the definition and some properties of \'etale sheaf complexes $\mathbb{Q}/\mathbb{Z}(j)$ on some schemes. The purpose of these notes is to be a precise reference for the Gersten conjecture of $\mathbb{Q}/\mathbb{Z}(j)$ over an imperfect field and also for the comparison between the cohomology groups $\mathrm{H}^2(\ast,\mathbb{Q}/\mathbb{Z}(1))$ and $\mathrm{H}^2(\ast,\mathbb{G}_m)$.

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Alexandre Lourdeaux. 2020-10-19. Faisceaux Q/Z(j) et conjecture de Gersten sur un corps imparfait. https://arxiv.org/abs/2010.09182

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