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PreprintCC BY 4.0arXiv

Brauer--Manin obstruction for Weil restrictions

  • Hui Zhang
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Abstract

For a quasi-projective variety X defined over a number field k, let X' be its Weil restriction with respect to a finite field extension k/k'. We prove that the Brauer--Manin set of X agrees with the Brauer--Manin set of X'. We also prove the agreement for Brauer--Manin set of them given by Br1.

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Cite

BibTeXRIS
BibTeX
@misc{zhang2026brauermanin,
  title = {{Brauer--Manin obstruction for Weil restrictions}},
  author = {Hui Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33736},
  eprint = {2610.33736},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33736},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Brauer--Manin obstruction for Weil restrictions
AU  - Hui Zhang
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33736
UR  - https://arxiv.org/abs/2610.33736
AB  - For a quasi-projective variety X defined over a number field k, let X' be its Weil restriction with respect to a finite field extension k/k'. We prove that the Brauer--Manin set of X agrees with the Brauer--Manin set of X'. We also prove the agreement for Brauer--Manin set of them given by Br_1.
ER  -