Seminar Algebra and Geometry: Eric Edo (Université de la Nouvelle Calédonie)

Generalisations of the tame automorphisms over a domain of positive characteristic

Joint work with S. Kuroda

Given a domain R of characteristic p >0, there exist two subgroups of the group GAn(R) of polynomial automorphisms which are natural generalisations of the linear group GL_n(R).

1) The subgroup of additive automorphisms, i.e. automorphisms with n components satisfying f(x+y) =f(x)+f(y) where x and y are set of n variables.

2) The subgroup of automorphisms with a Jacobian matrix in GL_n(R).

The subgroup generated by the translations and automorphisms of the type 1 (resp. 2) is called geometrically affine (resp. differentially affine). This group, together with the triangular automorphisms, generates the subgroup of geometrically tame (resp. differentially tame) automorphisms. We study these groups in dimension 2. We prove that they are different and endowed with a nice structure of amalgamated product.

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