TL;DR
This paper studies Vlasenko's formal group laws derived from Laurent polynomials, proving their integrality and linking their Frobenius matrices to Dieudonné modules in a p-adic setting.
Contribution
It identifies Vlasenko's formal group law with a formal group functor and establishes its integrality, connecting p-adic limits to Frobenius actions on Dieudonné modules.
Findings
Formal group law is identified with a coordinate system of a formal group functor.
Proves the integrality of Vlasenko's formal group law.
Shows the p-adic limit matrix is the Frobenius of the Dieudonné module.
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 \(p\).
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Algebra and Geometry