35 citations · 115 across the 21 of their papers we have counts for
23 papers
On endomorphisms of affine spaces and the Jacobian problem
Alexander Borisov, Ofer Gabber, Adrian Vasiu
Let be a prime. We provide examples which show that étale endomorphisms of affine planes over an algebraically closed field of characteristic can have fibers of arbitra…
Infinite transitivity of tame groups of automorphisms of affine spaces
Alexander Borisov, Ofer Gabber, Adrian Vasiu
For positive integers and , we study the actions of the groups of tame automorphisms of the -dimensional affine spaces over finite fields on ordered subsets of points…
A Structure Sheaf for Kirch Topology
Alexander Borisov
Kirch topology on goes back to 1969, and is remarkable for being Hausdorff, connected, and locally connected. In this sense, it is analogous to the usual topology on $\…
Frameworks for two-dimensional Keller maps
Alexander Borisov
A Keller map is a counterexample to the Jacobian Conjecture. In dimension two every such map, if exists, leads to a complicated set of conditions on the map between the Picard grou…
Geometrically Nilpotent Subvarieties
Alexander Borisov
We construct some examples of polynomial maps over finite fields that admit subvarieties with a peculiar property: every geometric point is mapped to a fixed point by some iteratio…
Some Interesting Integer Polynomial Maps
Alexander Borisov
We introduce three simple polynomial maps with integer coefficients that have interesting dynamical properties modulo primes.