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The tame and the wild automorphisms of polynomial rings in three variables
Author(s):
Ivan
P.
Shestakov;
Ualbai
U.
Umirbaev
Journal:
J. Amer. Math. Soc.
17
(2004),
197-227.
MSC (2000):
Primary 13F20, 13P10, 14H37;
Secondary 14R10, 14R15
Posted:
October 3, 2003
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Abstract:
A characterization of tame automorphisms of the algebra ![$A=F[x_1,x_2,x_3]$](/jams/2004-17-01/S0894-0347-03-00440-5/gif-abstract0/img1.gif) of polynomials in three variables over a field  of characteristic  is obtained. In particular, it is proved that the well-known Nagata automorphism is wild. It is also proved that the tame and the wild automorphisms of  are algorithmically recognizable.
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Additional Information:
Ivan
P.
Shestakov
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66281, São Paulo - SP, 05311--970, Brazil; Sobolev Institute of Mathematics, Novosibirsk, 630090, Russia
Email:
shestak@ime.usp.br
Ualbai
U.
Umirbaev
Affiliation:
Department of Mathematics, Eurasian National University, Astana, 473021, Kazakhstan
Email:
umirbaev@yahoo.com
DOI:
10.1090/S0894-0347-03-00440-5
PII:
S 0894-0347(03)00440-5
Keywords:
Rings of polynomials,
automorphisms,
subalgebras
Received by editor(s):
January 8, 2003
Posted:
October 3, 2003
Additional Notes:
The first author was supported by CNPq.
The second author was supported by the FAPESP Proc.00/06832-8.
Copyright of article:
Copyright
2003,
American Mathematical Society
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