English

On Vlasenko's formal group laws

Number Theory 2025-01-24 v1

Abstract

Given a Laurent polynomial over a ring flat over Z\mathbb{Z}, Vlasenko defines a formal group law. We identify this formal group law with a coordinate system of a formal group functor, prove its integrality. When the Hasse--Witt matrix of the Laurent polynomial is invertible, Vlasenko defines a matrix by taking a certain pp-adic limit. We show that this matrix is the Frobenius of the Dieudonn\'e module of this formal group modulo pp.

Keywords

Cite

@article{arxiv.2009.10512,
  title  = {On Vlasenko's formal group laws},
  author = {Dingxin Zhang},
  journal= {arXiv preprint arXiv:2009.10512},
  year   = {2025}
}
R2 v1 2026-06-23T18:43:06.127Z