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PreprintCC BY-SA 4.0arXiv

Integral Brauer--Manin Obstruction for Fermat Near Misses

  • Jessica Alessandrì
  • Jiazhi He
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Abstract

We study the integral Hasse principle for the affine surfaces given by x4+y4−w2=m2, where m>1 is odd and squarefree. We give a criterion to determine if there is an integral Brauer--Manin obstruction, which depends only on simple congruence conditions on the prime factors of m modulo $8$. We use this to show that for 100% of such surfaces there is no integral Brauer--Manin obstruction to the Hasse principle for integral points.

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Cite

BibTeXRIS
BibTeX
@misc{alessandri2026integral,
  title = {{Integral Brauer--Manin Obstruction for Fermat Near Misses}},
  author = {Jessica Alessandrì and Jiazhi He},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40815},
  eprint = {2610.40815},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40815},
  note = {CC BY-SA 4.0},
}
RIS
TY  - UNPB
TI  - Integral Brauer--Manin Obstruction for Fermat Near Misses
AU  - Jessica Alessandrì
AU  - Jiazhi He
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.40815
UR  - https://arxiv.org/abs/2610.40815
AB  - We study the integral Hasse principle for the affine surfaces given by x^4+y^4−w^2=m^2, where m>1 is odd and squarefree. We give a criterion to determine if there is an integral Brauer--Manin obstruction, which depends only on simple congruence conditions on the prime factors of m modulo $8$. We use this to show that for 100% of such surfaces there is no integral Brauer--Manin obstruction to the Hasse principle for integral points.
ER  -