Inverse limits of automorphisms of truncated polynomials and applications related to Jacobian conjecture

Abstract

In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic [Formula: see text]. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism [Formula: see text] of the polynomial ring [Formula: see text], if [Formula: see text] preserves the maximal ideals, then [Formula: see text] is an automorphism.