Obstruction sets and extensions of groups

Francesca Balestrieri

Acta Arithmetica, Tome 172 (2016), p. 151-181 / Harvested from The Polish Digital Mathematics Library

Résumé

Let X be a nice variety over a number field k. We characterise in pure “descent-type” terms some inequivalent obstruction sets refining the inclusion $X {(_{k})}^{é t, B r} \subset X {(_{k})}^{B r ₁}$ . In the first part, we apply ideas from the proof of $X {(_{k})}^{é t, B r} = X {(_{k})}^{_{k}}$ by Skorobogatov and Demarche to new cases, by proving a comparison theorem for obstruction sets. In the second part, we show that if $\subset \subset_{k}$ are such that $\subset E x t (,_{k})$ , then $X {(_{k})}^{} = X {(_{k})}^{}$ . This allows us to conclude, among other things, that $X {(_{k})}^{é t, B r} = X {(_{k})}^{_{k}}$ and $X {(_{k})}^{S o l, B r ₁} = X {(_{k})}^{S o l_{k}}$ .

Publié le : 2016-01-01

Zbl 06586880

EUDML-ID : urn:eudml:doc:279275

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     author = {Francesca Balestrieri},
     title = {Obstruction sets and extensions of groups},
     journal = {Acta Arithmetica},
     volume = {172},
     year = {2016},
     pages = {151-181},
     zbl = {06586880},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8154-12-2015}
}

Francesca Balestrieri. Obstruction sets and extensions of groups. Acta Arithmetica, Tome 172 (2016) pp. 151-181. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa8154-12-2015/