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PreprintarXiv licencearXiv

Comparing local-global obstructions on algebraic stacks

  • Chang Lv
  • Han Wu
  • Xucheng Zhang
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Abstract

Let k be a number field. For quotient stacks [X/G] with X a smooth quasi-projective geometrically integral k-variety and G a linear k-group, we extend several relations between local-global obstructions previously known for varieties, showing that étale-Brauer obstruction is the finest among various obstructions (such as iterated descent, finite descent, descent, Brauer-Manin).

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Cite

BibTeXRIS
BibTeX
@misc{lv2026comparing,
  title = {{Comparing local-global obstructions on algebraic stacks}},
  author = {Chang Lv and Han Wu and Xucheng Zhang},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.02141},
  eprint = {2608.02141},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.02141},
}
RIS
TY  - UNPB
TI  - Comparing local-global obstructions on algebraic stacks
AU  - Chang Lv
AU  - Han Wu
AU  - Xucheng Zhang
PY  - 2026
DA  - 2026/08/28
PB  - arXiv
DO  - 10.48550/arxiv.2608.02141
UR  - https://arxiv.org/abs/2608.02141
AB  - Let k be a number field. For quotient stacks [X/G] with X a smooth quasi-projective geometrically integral k-variety and G a linear k-group, we extend several relations between local-global obstructions previously known for varieties, showing that étale-Brauer obstruction is the finest among various obstructions (such as iterated descent, finite descent, descent, Brauer-Manin).
ER  -