Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

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

Hao Chang, Bin Shu, Yu-Feng Yao

Abstract

In this note, we investigate Jacobian conjecture through investigation of automorphisms of polynomial rings in characteristic $p$. Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism $\varphi$ of the polynomial ring $\mathbf{k}[x_1,\ldots,x_n]$, if $\varphi$ preserves the maximal ideals, then $\varphi$ is an automorphism.

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 . Making use of the technique of inverse limits, we show that under Jacobian condition for a given homomorphism of the polynomial ring , if preserves the maximal ideals, then is an automorphism.
Paper Structure (5 sections, 8 theorems, 10 equations)

This paper contains 5 sections, 8 theorems, 10 equations.

Table of Contents

  1. Jacobian Conjecture
  2. Characteristic $p$
  3. Inverse limits for truncated polynomials in characteristic $p$
  4. A strong Jacobian result in characteristic $p$
  5. A counterpart of Theorem \ref{['thm: Jac p']} in characteristic $0$

Key Result

Lemma 3.1

The automorphism group $\textsf{Aut}(R_s(\mathbf{a}))$ consists of ring homomorphisms $\sigma$ satisfying the following items

Theorems & Definitions (18)

  • Remark 1.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Lemma 3.4
  • proof
  • Proposition 3.5
  • ...and 8 more