Iterating the algebraic étale-Brauer set
In this paper, we iterate the algebraic étale-Brauer set for any nice variety X over a number field k with πét 1 (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 arithme...
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| Format: | Journal article |
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Elsevier
2017
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| Summary: | In this paper, we iterate the algebraic étale-Brauer set for any nice variety X over a number field k with πét 1 (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 on the arithmetic of rational points on K3 surfaces over k; moreover, it gives a partial answer to an “algebraic” analogue of a question by Poonen about iterating the descent set. |
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