Admissibility for special polynomial automorphisms beyond the tame subgroup

Determine under what conditions the flux class \([F^*\lambda-\lambda]\) is Cartier-admissible for a special polynomial automorphism \(F\in\operatorname{GA}_n(k)\) satisfying \(\det JF=1\), and establish whether every such special polynomial automorphism is Cartier-admissible.

Background

The main theorem proves Cartier-admissibility for every element of the special tame subgroup $\operatorname{STA}_n(k)$. The proof relies essentially on generation by special affine and elementary automorphisms, followed by closure of admissibility under products.

The paper gives an example showing that unrestricted Cartier iteration fails for arbitrary de Rham classes. It therefore leaves open how broadly the flux construction extends from special tame automorphisms to the full group of special polynomial automorphisms.