Details
| Original language | French |
|---|---|
| Pages (from-to) | 2151-2183 |
| Number of pages | 33 |
| Journal | Algebra and Number Theory |
| Volume | 14 |
| Issue number | 8 |
| Publication status | Published - 18 Sept 2020 |
Abstract
For a quasi-projective smooth geometrically integral variety over a number field k, we prove that the iterated descent obstruction is equivalent to the descent obstruction. This generalizes a result of Skorobogatov, and this answers an open question of Poonen. Our main tools are the notion of invariant Brauer subgroup and the notion of invariant étale Brauer–Manin obstruction for a k-variety equipped with an action of a connected linear algebraic group.
Keywords
- Algebraic group, Brauer–Manin obstruction, Hasse principle
ASJC Scopus subject areas
- Mathematics(all)
- Algebra and Number Theory
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In: Algebra and Number Theory, Vol. 14, No. 8, 18.09.2020, p. 2151-2183.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Sous-groupe de Brauer invariant et obstruction de descente itérée
AU - Cao, Yang
PY - 2020/9/18
Y1 - 2020/9/18
N2 - For a quasi-projective smooth geometrically integral variety over a number field k, we prove that the iterated descent obstruction is equivalent to the descent obstruction. This generalizes a result of Skorobogatov, and this answers an open question of Poonen. Our main tools are the notion of invariant Brauer subgroup and the notion of invariant étale Brauer–Manin obstruction for a k-variety equipped with an action of a connected linear algebraic group.
AB - For a quasi-projective smooth geometrically integral variety over a number field k, we prove that the iterated descent obstruction is equivalent to the descent obstruction. This generalizes a result of Skorobogatov, and this answers an open question of Poonen. Our main tools are the notion of invariant Brauer subgroup and the notion of invariant étale Brauer–Manin obstruction for a k-variety equipped with an action of a connected linear algebraic group.
KW - Algebraic group
KW - Brauer–Manin obstruction
KW - Hasse principle
UR - http://www.scopus.com/inward/record.url?scp=85094118090&partnerID=8YFLogxK
U2 - 10.48550/arXiv.1704.05425
DO - 10.48550/arXiv.1704.05425
M3 - Article
AN - SCOPUS:85094118090
VL - 14
SP - 2151
EP - 2183
JO - Algebra and Number Theory
JF - Algebra and Number Theory
SN - 1937-0652
IS - 8
ER -