Polynomial Automorphisms: And the Jacobian Conjecture

A-module Aff(R affine varieties algebraic set algebraically closed algebraically independent algorithm Applied Algebra assume Chapter characteristic zero coefficients commutative ring coordinate Corollary counterexample cubic homogeneous D₁ deduce defined deg F deg h deg Q degree denote dimension domain easily verifies eigenvalues elements embedding equivalent example Exercise exists F is invertible field of characteristic finitely generated k-algebra flat follows Furthermore Ga-action given gives Gröbner basis group actions H₁ hence Hubbers hypothesis ideal implies induction integer inverse function theorem irreducible isomorphism Jacobian Conjecture JF(x JH is nilpotent k-algebra Lemma Let F linear linearizable linearly locally finite locally nilpotent derivation map F Math matrix monomial morphism Newton polygons Noetherian non-zero observe polynomial automorphism polynomial map polynomial ring problem Proposition Pure and Applied resp result ring homomorphism satisfies semisimple Show strongly nilpotent suffices to prove surjective tends to infinity variables whence