Invariants and conjugacy classes of triangular polynomial maps

Stefan Maubach

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arXiv · 1307.6469

Invariants and conjugacy classes of triangular polynomial maps

Stefan Maubach

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Abstract

In this article, we classify invariants and conjugacy classes of triangular polynomial maps. We make these classifications in dimension 2 over domains containing $\Q$, dimension 2 over fields of characteristic $p$, and dimension 3 over fields of characteristic zero. We discuss the generic characteristic 0 case. We determine the invariants and conjugacy classes of strictly triangular maps of maximal order in all dimensions over fields of characteristic $p$. They turn out to be equivalent to a map of the form $(x_1+f_1,\ldots,x_n+f_n)$ where $f_i\in x_n^{p-1}k[x_{i+1}^p,\ldots,x_n^p]$ if $1\leq i\leq n-1$ and $f_n\in k^*$.

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Stefan Maubach. 2013-07-24. Invariants and conjugacy classes of triangular polynomial maps. https://arxiv.org/abs/1307.6469

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