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Iterating the algebraic étale-Brauer set

Abstract:

In this paper, we iterate the algebraic étale-Brauer set for any nice variety X over a number field k with πét 1 (X) finite and we show that the iterated set coincides with the original algebraic étale-Brauer set. This provides some evidence towards the conjectures by Colliot-Thélène on the arithmetic of rational points on nice geometrically rationally connected varieties over k and by Skorobogatov on the arithmetic of rational points on K3 surfaces over k; moreover, it gives a partial answe...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1016/j.jnt.2017.05.027

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Pembroke College
Role:
Author
Publisher:
Elsevier Publisher's website
Journal:
Journal of Number Theory Journal website
Volume:
182
Pages:
284-295
Publication date:
2017-07-20
Acceptance date:
2017-06-29
DOI:
EISSN:
1096-1658
ISSN:
0022-314X
Source identifiers:
707596
Keywords:
Pubs id:
pubs:707596
UUID:
uuid:0b101edb-24da-4964-bdc7-dcd95fbc5243
Local pid:
pubs:707596
Deposit date:
2017-07-10

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