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Obstruction sets and extensions of groups

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Balestrieri F.

Acta Arithmetica

2016

tom 173

nr 2

151-181

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 $X(𝔸_k)^{ét,Br} ⊂ X(𝔸_k)^{Br₁}$. In the first part, we apply ideas from the proof of $X(𝔸_k)^{ét,Br} = X(𝔸_k)^{𝓛_k}$ by Skorobogatov and Demarche to new cases, by proving a comparison theorem for obstruction sets. In the second part, we show that if $𝓐 ⊂ 𝓑 ⊂ 𝓛_k$ are such that $𝓑 ⊂ {Ext}(𝓐, 𝓤_k)$, then $X(𝔸_k)^{𝓐} = X(𝔸_k)^{𝓑}$. This allows us to conclude, among other things, that $X(𝔸_k)^{ét,Br} = X(𝔸_k)^{𝓡_k}$ and $X(𝔸_k)^{Sol,Br₁} = X(𝔸_k)^{Sol_k}$.

Ograniczanie wyników

1 Acta Arithmetica

1 Balestrieri F.

1 2016

Wyniki wyszukiwania

Obstruction sets and extensions of groups