We construct del Pezzo surfaces of degree violating the Hasse principle explained by the Brauer-Manin obstruction. Using these del Pezzo surfaces, we show that there are algebraic families of surfaces violating the Hasse principle explained by the Brauer-Manin obstruction. Various examples are given.
Nous construisons des surfaces de del Pezzo de degré violant le principe de Hasse expliqué par l’obstruction de Brauer-Manin. En utilisant ces surfaces de del Pezzo de degré , nous montrons qu’il y a des familles algébriques de surfaces violant le principe de Hasse expliqué par l’obstruction de Brauer-Manin. Divers exemples sont donnés.
@article{JTNB_2012__24_2_447_0,
author = {Dong Quan Ngoc Nguyen},
title = {The arithmetic of certain del {Pezzo} surfaces and {K3} surfaces},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {447--460},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {24},
number = {2},
year = {2012},
doi = {10.5802/jtnb.805},
mrnumber = {2950701},
zbl = {1268.14020},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.805/}
}
TY - JOUR AU - Dong Quan Ngoc Nguyen TI - The arithmetic of certain del Pezzo surfaces and K3 surfaces JO - Journal de théorie des nombres de Bordeaux PY - 2012 DA - 2012/// SP - 447 EP - 460 VL - 24 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.805/ UR - https://www.ams.org/mathscinet-getitem?mr=2950701 UR - https://zbmath.org/?q=an%3A1268.14020 UR - https://doi.org/10.5802/jtnb.805 DO - 10.5802/jtnb.805 LA - en ID - JTNB_2012__24_2_447_0 ER -
%0 Journal Article %A Dong Quan Ngoc Nguyen %T The arithmetic of certain del Pezzo surfaces and K3 surfaces %J Journal de théorie des nombres de Bordeaux %D 2012 %P 447-460 %V 24 %N 2 %I Société Arithmétique de Bordeaux %U https://doi.org/10.5802/jtnb.805 %R 10.5802/jtnb.805 %G en %F JTNB_2012__24_2_447_0
Dong Quan Ngoc Nguyen. The arithmetic of certain del Pezzo surfaces and K3 surfaces. Journal de théorie des nombres de Bordeaux, Volume 24 (2012) no. 2, pp. 447-460. doi : 10.5802/jtnb.805. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.805/
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