1982/01/01 by Hyman Bass, E. H. Connell, David L. Wright · 1 citation
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebra over a field #Applied mathematics #Arithmetic #Combinatorics #Conjecture #Degree (music) #Discrete mathematics #Inverse #Jacobian matrix and determinant #Law #Mathematical proof #Mathematics #Notation #Pure mathematics #Rank (graph theory) #Reduction (mathematics) #Statement (logic) #Unipotent
paper · pdf · doi:10.1090/s0273-0979-1982-15032-7
openalex publication_date 1982/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/08
Introduction I. The Jacobian Conjecture 1. Statement of the Jacobian Problem; first observations 2. Some history of the Jacobian Conjecture 3. Faulty proofs 4. The use of stabilization and of formal methods II. The Reduction Theorem 1. Notation 2. Statement of the Reduction Theorem 3. Reduction to degree 3 4. Proof of the Reduction Theorem 5. r-linearization and unipotent reduction 6. Nilpotent rank 1 Jacobians III. The Formal Inverse 1. Notation 2. Abhyankar's Inversion Formula 3. The terms Gj 4. The tree expansion G = lT(\/a(T))lfPTf 5. Calculations References