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In this paper, we iterate the algebraic étale-Brauer set for any nice variety X over a number field k with π1ét(X‾) finite and we show that the iterated set coincides with the original algebraic étale-Brauer set. This provides some evidence towards the conjectures by Colliot-Thélène on the arithmetic of rational points on nice geometrically rationally connected varieties over k and by Skorobogatov...
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