The ring of polynomial functors of prime degree

Abstract

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