The ring of polynomial functors of prime degree

Abstract

Let Z ^ p \hat {\mathbb {Z}}_p be the ring of p p -adic integers. We prove in the present paper that the category of polynomial functors from finitely generated free abelian groups to Z ^ p \hat {\mathbb {Z}}_p -modules of degree at most p p is equivalent to the category of modules over a particularly well understood ring, called Green order. This case was conjectured by Yuri Drozd.