Details
| Original language | English |
|---|---|
| Pages (from-to) | 8625-8650 |
| Number of pages | 26 |
| Journal | Transactions of the American Mathematical Society |
| Volume | 371 |
| Issue number | 12 |
| Publication status | Published - 2019 |
| Externally published | Yes |
Abstract
We provide a relation between Brauer-Manin obstruction and de- scent obstruction for torsors over not necessarily proper varieties under a con- nected linear algebraic group or a group of multiplicative type. Such a relation is also refined for torsors under a torus. The equivalence between descent ob- struction and étale Brauer-Manin obstruction for smooth projective varieties is extended to smooth quasi-projective varieties, which provides the perspective to study integral points.
Keywords
- Brauer-Manin obstruction, Descent obstruction, Linear algebraic group, Torsor
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Transactions of the American Mathematical Society, Vol. 371, No. 12, 2019, p. 8625-8650.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Comparing descent obstruction and Brauer-Manin obstruction for open varieties
AU - Cao, Yang
AU - Demarche, Cyril
AU - Xu, Fei
N1 - Funding information: Received by the editors November 18, 2016, and, in revised form, July 29, 2017 and November 28, 2017. 2010 Mathematics Subject Classification. Primary 14G05. Key words and phrases. Linear algebraic group, torsor, descent obstruction, Brauer-Manin obstruction. The first named author acknowledges the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-12-BL01-0005. The second named author acknowledges the support of the French Agence Nationale de la Recherche (ANR) under references ANR-12-BL01-0005 and ANR-15-CE40-0002-01. The third named author acknowledges the support of NSFC grants no. 11471219 and 11631009.
PY - 2019
Y1 - 2019
N2 - We provide a relation between Brauer-Manin obstruction and de- scent obstruction for torsors over not necessarily proper varieties under a con- nected linear algebraic group or a group of multiplicative type. Such a relation is also refined for torsors under a torus. The equivalence between descent ob- struction and étale Brauer-Manin obstruction for smooth projective varieties is extended to smooth quasi-projective varieties, which provides the perspective to study integral points.
AB - We provide a relation between Brauer-Manin obstruction and de- scent obstruction for torsors over not necessarily proper varieties under a con- nected linear algebraic group or a group of multiplicative type. Such a relation is also refined for torsors under a torus. The equivalence between descent ob- struction and étale Brauer-Manin obstruction for smooth projective varieties is extended to smooth quasi-projective varieties, which provides the perspective to study integral points.
KW - Brauer-Manin obstruction
KW - Descent obstruction
KW - Linear algebraic group
KW - Torsor
UR - http://www.scopus.com/inward/record.url?scp=85070257689&partnerID=8YFLogxK
U2 - 10.1090/tran/7567
DO - 10.1090/tran/7567
M3 - Article
AN - SCOPUS:85070257689
VL - 371
SP - 8625
EP - 8650
JO - Transactions of the American Mathematical Society
JF - Transactions of the American Mathematical Society
SN - 0002-9947
IS - 12
ER -