We investigate the question of whether the existence of a family of local zero-cycles of degree orthogonal to the Brauer group implies the non-emptiness of the Brauer–Manin set for certain varieties. We provide various examples of Brauer–Manin obstruction to the existence of zero-cycles of appropriate degrees.
Pour certaines variétés, nous étudions la question de savoir si l’existence d’une famille de zéro-cycles locaux de degré orthogonaux au groupe de Brauer implique la non-vacuité de l’ensemble de Brauer–Manin. Nous fournissons divers exemples d’obstructions de Brauer–Manin à l’existence de zéro-cycles de degrés appropriés.
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Keywords: Brauer–Manin obstruction, zero-cycles
Ieronymou, Evis 1
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@article{JTNB_2023__35_1_151_0,
author = {Ieronymou, Evis},
title = {Brauer{\textendash}Manin obstruction for zero-cycles on certain varieties},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {151--166},
year = {2023},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {35},
number = {1},
doi = {10.5802/jtnb.1241},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jtnb.1241/}
}
TY - JOUR AU - Ieronymou, Evis TI - Brauer–Manin obstruction for zero-cycles on certain varieties JO - Journal de théorie des nombres de Bordeaux PY - 2023 SP - 151 EP - 166 VL - 35 IS - 1 PB - Société Arithmétique de Bordeaux UR - https://www.numdam.org/articles/10.5802/jtnb.1241/ DO - 10.5802/jtnb.1241 LA - en ID - JTNB_2023__35_1_151_0 ER -
%0 Journal Article %A Ieronymou, Evis %T Brauer–Manin obstruction for zero-cycles on certain varieties %J Journal de théorie des nombres de Bordeaux %D 2023 %P 151-166 %V 35 %N 1 %I Société Arithmétique de Bordeaux %U https://www.numdam.org/articles/10.5802/jtnb.1241/ %R 10.5802/jtnb.1241 %G en %F JTNB_2023__35_1_151_0
Ieronymou, Evis. Brauer–Manin obstruction for zero-cycles on certain varieties. Journal de théorie des nombres de Bordeaux, Tome 35 (2023) no. 1, pp. 151-166. doi: 10.5802/jtnb.1241
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