Annals of K-Theory

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

Yang Cao

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Dans cet article, où le corps de base est un corps de caractéristique zéro quelconque, pour X une variété géométriquement cellulaire, on étudie le quotient du troisième groupe de cohomologie non ramifiée Hnr3(X,(2)) par sa partie constante. Pour X une compactification lisse d’un torseur universel sur une surface géométriquement rationnelle, on montre que ce quotient est fini. Pour X une surface de del Pezzo de degré 5, on montre que ce quotient est trivial, sauf si X est une surface de del Pezzo de degré 8 d’un type particulier.

We consider geometrically cellular varieties X over an arbitrary field of characteristic zero. We study the quotient of the third unramified cohomology group Hnr3(X,(2)) by its constant part. For X a smooth compactification of a universal torsor over a geometrically rational surface, we show that this quotient is finite. For X a del Pezzo surface of degree 5, we show that this quotient is zero, unless X is a del Pezzo surface of degree 8 of a special type.

Article information

Ann. K-Theory, Volume 3, Number 1 (2018), 157-171.

Received: 25 August 2016
Revised: 15 March 2017
Accepted: 2 April 2017
First available in Project Euclid: 20 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14E08: Rationality questions [See also 14M20] 19E15: Algebraic cycles and motivic cohomology [See also 14C25, 14C35, 14F42]

del Pezzo surface unramified cohomology


Cao, Yang. Cohomologie non ramifiée de degré 3 : variétés cellulaires et surfaces de del Pezzo de degré au moins 5. Ann. K-Theory 3 (2018), no. 1, 157--171. doi:10.2140/akt.2018.3.157.

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