Rational points and Brauer--Manin obstruction on Shimura varieties of level one classifying abelian varieties with quaternionic multiplication

Koji Matsuda

Rational points and Brauer--Manin obstruction on Shimura varieties of level one classifying abelian varieties with quaternionic multiplication

Number Theory 2024-07-10 v1

Authors: Koji Matsuda

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Abstract

We show that the Shimura varieties of level one parametrizing QM-abelian varieties have rarely rational points.

Keywords

Shimura varieties rational points Brauer-Manin obstruction abelian varieties quaternionic multiplication

Cite

@article{arxiv.2407.06921,
  title  = {Rational points and Brauer--Manin obstruction on Shimura varieties of level one classifying abelian varieties with quaternionic multiplication},
  author = {Koji Matsuda},
  journal= {arXiv preprint arXiv:2407.06921},
  year   = {2024}
}