Iterating the algebraic ├ętale-Brauer set

Francesca Balestrieri (University of Oxford)

Frank Adams 1,

We iterate the algebraic étale-Brauer set of a nice variety \(X\) over a number field \(k\) and show that, when the geometric étale fundamental group of \(X\) is finite, the iteration doesn't yield any new information. This result gives, among other things, evidence for the conjectures by Colliot-Thélène and Skorobogatov about the arithmetic behaviour of rational points on rationally connected varieties and K3 surfaces.
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