Non-existence of points rational over number fields on Shimura curves
Acta Arithmetica (2016)
- Volume: 172, Issue: 3, page 243-250
- ISSN: 0065-1036
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topKeisuke Arai. "Non-existence of points rational over number fields on Shimura curves." Acta Arithmetica 172.3 (2016): 243-250. <http://eudml.org/doc/279393>.
@article{KeisukeArai2016,
abstract = {Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.},
author = {Keisuke Arai},
journal = {Acta Arithmetica},
keywords = {rational points; Shimura curves; QM-abelian surfaces; Hasse principle},
language = {eng},
number = {3},
pages = {243-250},
title = {Non-existence of points rational over number fields on Shimura curves},
url = {http://eudml.org/doc/279393},
volume = {172},
year = {2016},
}
TY - JOUR
AU - Keisuke Arai
TI - Non-existence of points rational over number fields on Shimura curves
JO - Acta Arithmetica
PY - 2016
VL - 172
IS - 3
SP - 243
EP - 250
AB - Jordan, Rotger and de Vera-Piquero proved that Shimura curves have no points rational over imaginary quadratic fields under a certain assumption. In this article, we extend their results to the case of number fields of higher degree. We also give counterexamples to the Hasse principle on Shimura curves.
LA - eng
KW - rational points; Shimura curves; QM-abelian surfaces; Hasse principle
UR - http://eudml.org/doc/279393
ER -
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