Obstruction sets and extensions of groups

• Autorzy: Francesca Balestrieri
• Języki publikacji: EN

Abstrakty

EN

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 $X(𝔸_k)^{Sol,Br₁} = X(𝔸_k)^{Sol_k}$.

Kategorie tematyczne

• 11G35: Varieties over global fields
• 20G30: Linear algebraic groups over global fields and their integers
• 14G05: Rational points

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2016
• Tom: 173
• Numer: 2
• Strony: 151-181

Daty

wydano

2016

Twórcy

autor

Francesca Balestrieri

• Mathematical Institute, Oxford, OX2 6HD, United Kingdom

Identyfikatory

DOI

10.4064/aa8154-12-2015