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

Abstract

We consider geometrically cellular varieties $X$ over an arbitrary field of characteristic zero. We study the quotient of the third unramified cohomology group $H_{nr}^3(X,\mathbb{Q}/\mathbb{Z}(2))$ 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 $\ge 5$, we show that this quotient is zero, unless $X$ is a del Pezzo surface of degree 8 of a special type.

In French

References in corpus (1)

• Semiorthogonal decompositions and birational geometry of del Pezzo surfaces over arbitrary fields