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Integrality of height-one formal groups

  • Martin Debaisieux
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Abstract

Let K be a finite extension of ℚp. We prove that a one-dimensional formal group law over K has integral coefficients if and only if its multiplication-by-n endomorphisms have integral coefficients for all integers n, in the height-one case, that is when the multiplication by p has Weierstrass degree p. The proof relies on p-adic Hodge theory.

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Cite

BibTeXRIS
BibTeX
@misc{debaisieux2026integrality,
  title = {{Integrality of height-one formal groups}},
  author = {Martin Debaisieux},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2606.25726},
  eprint = {2606.25726},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2606.25726},
}
RIS
TY  - UNPB
TI  - Integrality of height-one formal groups
AU  - Martin Debaisieux
PY  - 2026
DA  - 2026/11/03
PB  - arXiv
DO  - 10.48550/arxiv.2606.25726
UR  - https://arxiv.org/abs/2606.25726
AB  - Let K be a finite extension of ℚ_p. We prove that a one-dimensional formal group law over K has integral coefficients if and only if its multiplication-by-n endomorphisms have integral coefficients for all integers n, in the height-one case, that is when the multiplication by p has Weierstrass degree p. The proof relies on p-adic Hodge theory.
ER  -