Computation of the classifying ring of formal modules

TL;DR

This paper introduces a general method for computing the classifying ring of one-dimensional formal modules over various rings, including number rings and cyclic group rings, with new calculations where the ring is not polynomial.

Contribution

Develops a general machinery for computing classifying rings of formal modules and applies it to new cases, including non-polynomial rings.

Findings

First full calculations of $L^A$ for certain rings where it is not polynomial

Provides insights into lifting and extension problem solvability

Calculates classifying rings for number and cyclic group rings

Abstract

In this paper, we develop general machinery for computing the classifying ring $L^A$ of one-dimensional formal $A$-modules, for various commutative rings $A$. We then apply the machinery to obtain calculations of $L^A$ for various number rings and cyclic group rings $A$. This includes the first full calculations of the ring $L^A$ in cases in which it fails to be a polynomial algebra. We also derive consequences for the solvability of some lifting and extension problems.