Author

A. Borisov

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Preprint Aug 2026

Infinite transitivity of tame groups of automorphisms of affine spaces

For positive integers $n$ and $m$, we study the actions of the groups of tame automorphisms of the $n$-dimensional affine spaces over finite fields on ordered subsets of $m$ points. Our primary interest lies in constructing tame automorphisms that take one ordered sequence to another and in proving upper and lower boun...

A. Borisov, O. Gabber, A. Vasiu · 0 citations

Preprint Sep 2026

On endomorphisms of affine spaces and the Jacobian problem

Let $p$ be a prime. We provide examples which show that \'etale endomorphisms of affine planes over an algebraically closed field $k$ of characteristic $p$ can have fibers of arbitrary finite cardinal. Let $(l,m)\in\mathbb N\times\mathbb N^{\ast}$. We provide examples of such \'etale endomorphisms whose images have com...

A. Borisov, O. Gabber, A. Vasiu · 1 citation