Homogeneous spaces with transcendental Brauer--Manin obstruction to the Hasse principle

@misc{linh2026homogeneous,
  title = {{Homogeneous spaces with transcendental Brauer--Manin obstruction to the Hasse principle}},
  author = {Nguyen Manh Linh},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2606.09214},
  eprint = {2606.09214},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.09214},
  note = {CC BY 4.0},
}

TY  - UNPB
TI  - Homogeneous spaces with transcendental Brauer--Manin obstruction to the Hasse principle
AU  - Nguyen Manh Linh
PY  - 2026
DA  - 2026/10/22
PB  - arXiv
DO  - 10.48550/arxiv.2606.09214
UR  - https://arxiv.org/abs/2606.09214
AB  - Over any number field with sufficiently many roots of unity, we construct homogeneous spaces of SL_n with finite geometric stabilizers of nilpotency class $2$, whose unramified algebraic Brauer group consists only of constant classes, and which has no rational point but has local points in every completion of the ground field. This provides the first known examples of failures of the Hasse principle for homogeneous spaces of connected linear algebraic groups that are detected only by transcendental Brauer classes. The construction builds on the failure of a global--local principle for cup-product decomposition, based on a previous idea of Borovoi and Kunyavskii.
ER  -