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PreprintCC BY 4.0arXiv

The linear positive torsor presentation and arithmetic purity of strong approximation

  • Yijin Wang
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Abstract

In this article, we define a notion for varieties called linear positive torsor presentation. For varieties with a linear positive torsor presentation over number fields, we establish the arithmetic purity of strong approximation with the Brauer--Manin obstruction off the empty set. As a consequence, we recover arithmetic purity for smooth toric variety with no non-constant global section. Moreover, we classify the chain connected class for rational points on such varieties over any field of characteristic zero.

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Cite

BibTeXRIS
BibTeX
@misc{wang2026linear,
  title = {{The linear positive torsor presentation and arithmetic purity of strong approximation}},
  author = {Yijin Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.21762},
  eprint = {2610.21762},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.21762},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The linear positive torsor presentation and arithmetic purity of strong approximation
AU  - Yijin Wang
PY  - 2026
DA  - 2026/10/15
PB  - arXiv
DO  - 10.48550/arxiv.2610.21762
UR  - https://arxiv.org/abs/2610.21762
AB  - In this article, we define a notion for varieties called linear positive torsor presentation. For varieties with a linear positive torsor presentation over number fields, we establish the arithmetic purity of strong approximation with the Brauer--Manin obstruction off the empty set. As a consequence, we recover arithmetic purity for smooth toric variety with no non-constant global section. Moreover, we classify the chain connected class for rational points on such varieties over any field of characteristic zero.
ER  -