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arXiv · 1607.01739

Cohomologie non ramifiée de degré 3 : variétés cellulaires et surfaces de del Pezzo de degré au moins 5

Yang Cao
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Abstract

We consider geometrically cellular varieties $X$ over an arbitrary field of characteristic zero. We study the quotient of the third unramified cohomology group $H^3_{nr}(X,\mathbb{Q}/\mathbb{Z}(2))$ by its constant part. For $X$ a smooth compactification of a universal torsor over a geometrically rational surface, we show that this quotient if finite. For $X$ a del Pezzo surface of degree $\geq 5$, we show that this quotient is zero, unless $X$ is a del Pezzo surface of degree 8 of a special type.

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Yang Cao. 2016-08-25. Cohomologie non ramifiée de degré 3 : variétés cellulaires et surfaces de del Pezzo de degré au moins 5. https://doi.org/10.2140/akt.2018.3.157

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