Operations on integral lifts of K(n)

TL;DR

This paper explores the structure of operations on integral lifts of K(n) in cohomology theories over valuation rings, revealing their extension properties related to automorphism groups and exterior algebras.

Contribution

It provides new insights into the algebraic structure of operations on lifts of K(n) in the context of local number fields and Lubin-Tate groups.

Findings

Operations form extensions of automorphism groups

Extensions involve exterior algebras on normal bundles

Evidence supports a specific algebraic structure hypothesis

Abstract

This very rough sketch is a sequel to arXiv:1808.08587; it presents evidence that operations on lifts of the functors K(n) to cohomology theories with values in modules over valuation rings of local number fields, indexed by Lubin-Tate groups of such fields, are extensions of the groups of automorphisms of the indexing group laws, by the exterior algebras on the normal bundle to the orbits of the group laws in the space of lifts.