The Nagata automorphism is wild.
It is proved that the well known Nagata automorphism of the polynomial ring in three variables over a field of characteristic zero is wild, that is, it can not be decomposed into a product of elementary automorphisms.
Shestakov
Ivan P
IP
Instituto de Matemática e Estatistica, Universidade de São Paulo, Caixa Postal 66281, São Paulo, SP 05311-970, Brazil. shestak@ime.usp.br
Umirbaev
Ualbai U
UU