On Vlasenko's formal group laws

Abstract

Given a Laurent polynomial over a ring flat over \(\mathbb{Z}\), 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 \(p\)-adic limit. We show that this matrix is the Frobenius of the Dieudonn\'e module of this formal group modulo \(p\).